31 + Interview Questions in Abaxis Aptitude Interview Questions in Abaxis Aptitude Tutorial Page 1 InterviewSolution

1.	There Is A Group Of Persons Each Of Whom Can Complete A Piece Of Work In 16 Days, When They Are Working Individually. On The First Day One Person Works, On The Second Day Another Person Joins Him, On The Third Day One More Person Joins Them And This Process Continues Till The Work Is Completed. How Many Days Are Needed To Complete The Work?
Answer» WORK COMPLETED in 1ST DAY = 1/16 Work completed in 2nd day = (1/16) + (1/16) = 2/16 Work completed in 3RD day = (1/16) + (1/16) + (1/16) = 3/16 Work completed in 1st day = 1/16 Work completed in 2nd day = (1/16) + (1/16) = 2/16 Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16

1.

There Is A Group Of Persons Each Of Whom Can Complete A Piece Of Work In 16 Days, When They Are Working Individually. On The First Day One Person Works, On The Second Day Another Person Joins Him, On The Third Day One More Person Joins Them And This Process Continues Till The Work Is Completed. How Many Days Are Needed To Complete The Work?

Answer»

WORK COMPLETED in 1ST DAY = 1/16

Work completed in 2nd day = (1/16) + (1/16) = 2/16

Work completed in 3RD day = (1/16) + (1/16) + (1/16) = 3/16

Work completed in 1st day = 1/16

Work completed in 2nd day = (1/16) + (1/16) = 2/16

Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16

Discussion

2.	Assume That 20 Cows And 40 Goats Can Be Kept For 10 Days For Rs.460. If The Cost Of Keeping 5 Goats Is The Same As The Cost Of Keeping 1 Cow, What Will Be The Cost For Keeping 50 Cows And 30 Goats For 12 Days ?
Answer» Assume that cost of keeping a cow for 1 day = c , cost of keeping a goat for 1 day = g Cost of keeping 20 cows and 40 goats for 10 days = 460 Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46 =&GT; 20c + 40g = 46 => 10c + 20g = 23 ---(1) Given that 5g = c Hence equation (1) can be written as 10c + 4c = 23 => 14c =23 => c=23/14 cost of keeping 50 cows and 30 goats for 1 day = 50c + 30G = 50c + 6c (substituted 5g = c) = 56 c = 56×23/14 = 92 Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104 Assume that cost of keeping a cow for 1 day = c , cost of keeping a goat for 1 day = g Cost of keeping 20 cows and 40 goats for 10 days = 460 Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46 => 20c + 40g = 46 => 10c + 20g = 23 ---(1) Given that 5g = c Hence equation (1) can be written as 10c + 4c = 23 => 14c =23 => c=23/14 cost of keeping 50 cows and 30 goats for 1 day = 50c + 30g = 50c + 6c (substituted 5g = c) = 56 c = 56×23/14 = 92 Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104

2.

Assume That 20 Cows And 40 Goats Can Be Kept For 10 Days For Rs.460. If The Cost Of Keeping 5 Goats Is The Same As The Cost Of Keeping 1 Cow, What Will Be The Cost For Keeping 50 Cows And 30 Goats For 12 Days ?

Answer»

Assume that cost of keeping a cow for 1 day = c ,

cost of keeping a goat for 1 day = g

Cost of keeping 20 cows and 40 goats for 10 days = 460

Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46

=&GT; 20c + 40g = 46

=> 10c + 20g = 23 ---(1)

Given that 5g = c

Hence equation (1) can be written as 10c + 4c = 23 => 14c =23

=> c=23/14

cost of keeping 50 cows and 30 goats for 1 day

= 50c + 30G

= 50c + 6c (substituted 5g = c)

= 56 c = 56×23/14

= 92

Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104

Assume that cost of keeping a cow for 1 day = c ,

cost of keeping a goat for 1 day = g

Cost of keeping 20 cows and 40 goats for 10 days = 460

Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46

=> 20c + 40g = 46

=> 10c + 20g = 23 ---(1)

Given that 5g = c

Hence equation (1) can be written as 10c + 4c = 23 => 14c =23

=> c=23/14

cost of keeping 50 cows and 30 goats for 1 day

= 50c + 30g

= 50c + 6c (substituted 5g = c)

= 56 c = 56×23/14

= 92

Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104

Discussion

3.	P,q And R Together Earn Rs.1620 In 9 Days. P And R Can Earn Rs.600 In 5 Days. Q And R In 7 Days Can Earn Rs.910. How Much Amount Does R Can Earn Per Day ?
Answer» AMOUNT EARNED by P,Q and R in 1 day = 1620/9 = 180 ---(1) Amount Earned by P and R in 1 day = 600/5 = 120 ---(2) Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3) (2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day - Amount Earned by P,Q and R in 1 day = 120+130-180 = 70 =>Amount Earned by R in 1 day = 70 Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1) Amount Earned by P and R in 1 day = 600/5 = 120 ---(2) Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3) (2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day - Amount Earned by P,Q and R in 1 day = 120+130-180 = 70 =>Amount Earned by R in 1 day = 70

3.

P,q And R Together Earn Rs.1620 In 9 Days. P And R Can Earn Rs.600 In 5 Days. Q And R In 7 Days Can Earn Rs.910. How Much Amount Does R Can Earn Per Day ?

Answer»

AMOUNT EARNED by P,Q and R in 1 day = 1620/9 = 180 ---(1)

Amount Earned by P and R in 1 day = 600/5 = 120 ---(2)

Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3)

(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day

- Amount Earned by P,Q and R in 1 day = 120+130-180 = 70

=>Amount Earned by R in 1 day = 70

Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)

Amount Earned by P and R in 1 day = 600/5 = 120 ---(2)

Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3)

(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day

- Amount Earned by P,Q and R in 1 day = 120+130-180 = 70

=>Amount Earned by R in 1 day = 70

Discussion

4.	If Daily Wages Of A Man Is Double To That Of A Woman, How Many Men Should Work For 25 Days To Earn Rs.14400? Given That Wages For 40 Women For 30 Days Are Rs.21600.
Answer» WAGES of 1 WOMAN for 1 day = 2160040×30 Wages of 1 man for 1 day = 21600×240×30 Wages of 1 man for 25 days = 21600×2×2540×30 NUMBER of men = 14400(21600×2×2540×30)=144(216×5040×30)=1449=16 Wages of 1 woman for 1 day = 2160040×30 Wages of 1 man for 1 day = 21600×240×30 Wages of 1 man for 25 days = 21600×2×2540×30 Number of men = 14400(21600×2×2540×30)=144(216×5040×30)=1449=16

4.

If Daily Wages Of A Man Is Double To That Of A Woman, How Many Men Should Work For 25 Days To Earn Rs.14400? Given That Wages For 40 Women For 30 Days Are Rs.21600.

Answer»

WAGES of 1 WOMAN for 1 day = 2160040×30

Wages of 1 man for 1 day = 21600×240×30

Wages of 1 man for 25 days = 21600×2×2540×30

NUMBER of men = 14400(21600×2×2540×30)=144(216×5040×30)=1449=16

Wages of 1 woman for 1 day = 2160040×30

Wages of 1 man for 1 day = 21600×240×30

Wages of 1 man for 25 days = 21600×2×2540×30

Number of men = 14400(21600×2×2540×30)=144(216×5040×30)=1449=16

Discussion

5.	P Can Do A Work In 24 Days. Q Can Do The Same Work In 9 Days And R Can Do The Same In 12 Days. Q And R Start The Work And Leave After 3 Days. P Finishes The Remaining Work In --- Days.
Answer» Work done by P in 1 DAY = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3×7/36 = 7/12 Remaining work = 1 – 7/12 = 5/12 NUMBER of days in which P can FINISH the remaining work = (5/12) / (1/24) = 10 Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/9 Work done by R in 1 day = 1/12 Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36 Work done by Q and R in 3 days = 3×7/36 = 7/12 Remaining work = 1 – 7/12 = 5/12 Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10

5.

P Can Do A Work In 24 Days. Q Can Do The Same Work In 9 Days And R Can Do The Same In 12 Days. Q And R Start The Work And Leave After 3 Days. P Finishes The Remaining Work In --- Days.

Answer»

Work done by P in 1 DAY = 1/24

Work done by Q in 1 day = 1/9

Work done by R in 1 day = 1/12

Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36

Work done by Q and R in 3 days = 3×7/36 = 7/12

Remaining work = 1 – 7/12 = 5/12

NUMBER of days in which P can FINISH the remaining work = (5/12) / (1/24) = 10

Work done by P in 1 day = 1/24

Work done by Q in 1 day = 1/9

Work done by R in 1 day = 1/12

Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36

Work done by Q and R in 3 days = 3×7/36 = 7/12

Remaining work = 1 – 7/12 = 5/12

Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10

Discussion

6.	P And Q Need 8 Days To Complete A Work. Q And R Need 12 Days To Complete The Same Work. But P, Q And R Together Can Finish It In 6 Days. How Many Days Will Be Needed If P And R Together Do It ?
Answer» Let work done by P in 1 day = p work done by Q in 1 day =q Work done by R in 1 day = r p + q = 1/8 ---(1) q + r= 1/12 ---(2) p+ q+ r = 1/6 ---(3) (3) – (2) => p = 1/6 - 1/12 = 1/12 (3) – (1) => r = 1/6 – 1/8 = 1/24 p + r = 1/12 + 1/24 = 3/24 = 1/8 => P and R will FINISH the work in 8 DAYS Let work done by P in 1 day = p work done by Q in 1 day =q Work done by R in 1 day = r p + q = 1/8 ---(1) q + r= 1/12 ---(2) p+ q+ r = 1/6 ---(3) (3) – (2) => p = 1/6 - 1/12 = 1/12 (3) – (1) => r = 1/6 – 1/8 = 1/24 p + r = 1/12 + 1/24 = 3/24 = 1/8 => P and R will finish the work in 8 days

6.

P And Q Need 8 Days To Complete A Work. Q And R Need 12 Days To Complete The Same Work. But P, Q And R Together Can Finish It In 6 Days. How Many Days Will Be Needed If P And R Together Do It ?

Answer»

Let work done by P in 1 day = p

work done by Q in 1 day =q

Work done by R in 1 day = r

p + q = 1/8 ---(1)

q + r= 1/12 ---(2)

p+ q+ r = 1/6 ---(3)

(3) – (2) => p = 1/6 - 1/12 = 1/12

(3) – (1) => r = 1/6 – 1/8 = 1/24

p + r = 1/12 + 1/24 = 3/24 = 1/8

=> P and R will FINISH the work in 8 DAYS

Let work done by P in 1 day = p

work done by Q in 1 day =q

Work done by R in 1 day = r

p + q = 1/8 ---(1)

q + r= 1/12 ---(2)

p+ q+ r = 1/6 ---(3)

(3) – (2) => p = 1/6 - 1/12 = 1/12

(3) – (1) => r = 1/6 – 1/8 = 1/24

p + r = 1/12 + 1/24 = 3/24 = 1/8

=> P and R will finish the work in 8 days

Discussion

7.	A Work Can Be Finished In 16 Days By Twenty Women. The Same Work Can Be Finished In Fifteen Days By Sixteen Men. The Ratio Between The Capacity Of A Man And A Woman Is
Answer» WORK done by 20 women in 1 DAY = 1/16 Work done by 1 woman in 1 day = 1/(16×20) Work done by 16 MEN in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×16) Ratio of the CAPACITY of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20 = 1/3 :1/4 = 4:3 Work done by 20 women in 1 day = 1/16 Work done by 1 woman in 1 day = 1/(16×20) Work done by 16 men in 1 day = 1/15 Work done by 1 man in 1 day = 1/(15×16) Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20 = 1/3 :1/4 = 4:3

7.

A Work Can Be Finished In 16 Days By Twenty Women. The Same Work Can Be Finished In Fifteen Days By Sixteen Men. The Ratio Between The Capacity Of A Man And A Woman Is

Answer»

WORK done by 20 women in 1 DAY = 1/16

Work done by 1 woman in 1 day = 1/(16×20)

Work done by 16 MEN in 1 day = 1/15

Work done by 1 man in 1 day = 1/(15×16)

Ratio of the CAPACITY of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20

= 1/3 :1/4 = 4:3

Work done by 20 women in 1 day = 1/16

Work done by 1 woman in 1 day = 1/(16×20)

Work done by 16 men in 1 day = 1/15

Work done by 1 man in 1 day = 1/(15×16)

Ratio of the capacity of a man and woman =1/(15×16) : 1/(16×20) = 1/15 : 1/20

= 1/3 :1/4 = 4:3

Discussion

8.	P Works Twice As Fast As Q. If Q Alone Can Complete A Work In 12 Days, P And Q Can Finish The Work In --- Days
Answer» WORK done by Q in 1 DAY = 1/12 Work done by P in 1 day = 2 × (1/12) = 1/6 Work done by P and Q in 1 day = 1/12 + 1/6 = ¼ => P and Q can finish the work in 4 DAYS Work done by Q in 1 day = 1/12 Work done by P in 1 day = 2 × (1/12) = 1/6 Work done by P and Q in 1 day = 1/12 + 1/6 = ¼ => P and Q can finish the work in 4 days

8.

P Works Twice As Fast As Q. If Q Alone Can Complete A Work In 12 Days, P And Q Can Finish The Work In --- Days

Answer»

WORK done by Q in 1 DAY = 1/12

Work done by P in 1 day = 2 × (1/12) = 1/6

Work done by P and Q in 1 day = 1/12 + 1/6 = ¼

=> P and Q can finish the work in 4 DAYS

Work done by Q in 1 day = 1/12

Work done by P in 1 day = 2 × (1/12) = 1/6

Work done by P and Q in 1 day = 1/12 + 1/6 = ¼

=> P and Q can finish the work in 4 days

Discussion

9.	P And Q Can Do A Work In 30 Days. Q And R Can Do The Same Work In 24 Days And R And P In 20 Days. They Started The Work Together, But Q And R Left After 10 Days. How Many Days More Will P Take To Finish The Work ?
Answer» LET work done by P in 1 day = p, Work done by Q in 1 day = q, Work done by R in 1 day = r p + q = 1/30 q + r = 1/24 r + p = 1/20 Adding all the above, 2P + 2Q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8 => p + q + r = 1/16 => Work done by P,Q and R in 1 day = 1/16 Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8 Remaining work = 1 = 5/8 = 3/8 Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day = 1/16 – 1/24 = 1/48 Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18 Let work done by P in 1 day = p, Work done by Q in 1 day = q, Work done by R in 1 day = r p + q = 1/30 q + r = 1/24 r + p = 1/20 Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8 => p + q + r = 1/16 => Work done by P,Q and R in 1 day = 1/16 Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8 Remaining work = 1 = 5/8 = 3/8 Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day = 1/16 – 1/24 = 1/48 Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

9.

P And Q Can Do A Work In 30 Days. Q And R Can Do The Same Work In 24 Days And R And P In 20 Days. They Started The Work Together, But Q And R Left After 10 Days. How Many Days More Will P Take To Finish The Work ?

Answer»

LET work done by P in 1 day = p,

Work done by Q in 1 day = q,

Work done by R in 1 day = r

p + q = 1/30

q + r = 1/24

r + p = 1/20

Adding all the above, 2P + 2Q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8

=> p + q + r = 1/16

=> Work done by P,Q and R in 1 day = 1/16

Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8

Remaining work = 1 = 5/8 = 3/8

Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day

= 1/16 – 1/24 = 1/48

Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

Let work done by P in 1 day = p,

Work done by Q in 1 day = q,

Work done by R in 1 day = r

p + q = 1/30

q + r = 1/24

r + p = 1/20

Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8

=> p + q + r = 1/16

=> Work done by P,Q and R in 1 day = 1/16

Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8

Remaining work = 1 = 5/8 = 3/8

Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day

= 1/16 – 1/24 = 1/48

Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18

Discussion

10.	P And Q Can Complete A Work In 15 Days And 10 Days Respectively. They Started The Work Together And Then Q Left After 2 Days. P Alone Completed The Remaining Work. The Work Was Finished In --- Days.
Answer» WORK DONE by P in 1 day = 1/15 Work done by Q in 1 day = 1/10 Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6 Work done by P and Q in 2 DAYS = 2 × (1/6) = 1/3 Remaining work = 1 – 1/3 = 2/3 Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days TOTAL time taken = 2 + 10 = 12 days Work done by P in 1 day = 1/15 Work done by Q in 1 day = 1/10 Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6 Work done by P and Q in 2 days = 2 × (1/6) = 1/3 Remaining work = 1 – 1/3 = 2/3 Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days Total time taken = 2 + 10 = 12 days

10.

P And Q Can Complete A Work In 15 Days And 10 Days Respectively. They Started The Work Together And Then Q Left After 2 Days. P Alone Completed The Remaining Work. The Work Was Finished In --- Days.

Answer»

WORK DONE by P in 1 day = 1/15

Work done by Q in 1 day = 1/10

Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6

Work done by P and Q in 2 DAYS = 2 × (1/6) = 1/3

Remaining work = 1 – 1/3 = 2/3

Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days

TOTAL time taken = 2 + 10 = 12 days

Work done by P in 1 day = 1/15

Work done by Q in 1 day = 1/10

Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6

Work done by P and Q in 2 days = 2 × (1/6) = 1/3

Remaining work = 1 – 1/3 = 2/3

Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days

Total time taken = 2 + 10 = 12 days

Discussion

11.	P Takes Twice As Much Time As Q Or Thrice As Much Time As R To Finish A Piece Of Work. They Can Finish The Work In 2 Days If Work Together. How Much Time Will Q Take To Do The Work Alone ?
Answer» LET P takes x days to complete the work Then Q takes x/2 days and R takes x/3 days to FINISH the work AMOUNT of work P does in 1 day = 1/x Amount of work Q does in 1 day = 2/x Amount of work R does in 1 day = 3/x Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x 6/x = 2 => x = 12 => Q takes 12/2 days = 6 days to complete the work. Let P takes x days to complete the work Then Q takes x/2 days and R takes x/3 days to finish the work Amount of work P does in 1 day = 1/x Amount of work Q does in 1 day = 2/x Amount of work R does in 1 day = 3/x Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x 6/x = 2 => x = 12 => Q takes 12/2 days = 6 days to complete the work.

11.

P Takes Twice As Much Time As Q Or Thrice As Much Time As R To Finish A Piece Of Work. They Can Finish The Work In 2 Days If Work Together. How Much Time Will Q Take To Do The Work Alone ?

Answer»

LET P takes x days to complete the work

Then Q takes x/2 days and R takes x/3 days to FINISH the work

AMOUNT of work P does in 1 day = 1/x

Amount of work Q does in 1 day = 2/x

Amount of work R does in 1 day = 3/x

Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x

6/x = 2

=> x = 12

=> Q takes 12/2 days = 6 days to complete the work.

Let P takes x days to complete the work

Then Q takes x/2 days and R takes x/3 days to finish the work

Amount of work P does in 1 day = 1/x

Amount of work Q does in 1 day = 2/x

Amount of work R does in 1 day = 3/x

Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x

6/x = 2

=> x = 12

=> Q takes 12/2 days = 6 days to complete the work.

Discussion

12.	P And Q Can Complete A Work In 20 Days And 12 Days Respectively. P Alone Started The Work And Q Joined Him After 4 Days Till The Completion Of The Work. How Long Did The Work Last ?
Answer» Work DONE by P in 1 DAY = 1/20 Work done by Q in 1 day = 1/12 Work done by P in 4 days = 4 × (1/20) = 1/5 Remaining work = 1 – 1/5 = 4/5 Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15 Number of days P and Q take to COMPLETE the remaining work = (4/5) / (2/15) = 6 Total days = 4 + 6 = 10 Work done by P in 1 day = 1/20 Work done by Q in 1 day = 1/12 Work done by P in 4 days = 4 × (1/20) = 1/5 Remaining work = 1 – 1/5 = 4/5 Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15 Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6 Total days = 4 + 6 = 10

12.

P And Q Can Complete A Work In 20 Days And 12 Days Respectively. P Alone Started The Work And Q Joined Him After 4 Days Till The Completion Of The Work. How Long Did The Work Last ?

Answer»

Work DONE by P in 1 DAY = 1/20

Work done by Q in 1 day = 1/12

Work done by P in 4 days = 4 × (1/20) = 1/5

Remaining work = 1 – 1/5 = 4/5

Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15

Number of days P and Q take to COMPLETE the remaining work = (4/5) / (2/15) = 6

Total days = 4 + 6 = 10

Work done by P in 1 day = 1/20

Work done by Q in 1 day = 1/12

Work done by P in 4 days = 4 × (1/20) = 1/5

Remaining work = 1 – 1/5 = 4/5

Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15

Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6

Total days = 4 + 6 = 10

Discussion

13.	Anil And Suresh Are Working On A Special Assignment. Anil Needs 6 Hours To Type 32 Pages On A Computer And Suresh Needs 5 Hours To Type 40 Pages. If Both Of Them Work Together On Two Different Computers, How Much Time Is Needed To Type An Assignment Of 110 Pages ?
Answer» PAGES typed by Anil in 1 hour = 32/6 = 16/3 Pages typed by Suresh in 1 hour = 40/5 = 8 Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3 Time taken to type 110 pages when Anil and Suresh work TOGETHER = 110 × 3 /40 = 33/4 = 8 1/4 hours = 8 hour 15 MINUTES Pages typed by Anil in 1 hour = 32/6 = 16/3 Pages typed by Suresh in 1 hour = 40/5 = 8 Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3 Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4 = 8 1/4 hours = 8 hour 15 minutes

13.

Anil And Suresh Are Working On A Special Assignment. Anil Needs 6 Hours To Type 32 Pages On A Computer And Suresh Needs 5 Hours To Type 40 Pages. If Both Of Them Work Together On Two Different Computers, How Much Time Is Needed To Type An Assignment Of 110 Pages ?

Answer»

PAGES typed by Anil in 1 hour = 32/6 = 16/3

Pages typed by Suresh in 1 hour = 40/5 = 8

Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3

Time taken to type 110 pages when Anil and Suresh work TOGETHER = 110 × 3 /40 = 33/4

= 8 1/4 hours = 8 hour 15 MINUTES

Pages typed by Anil in 1 hour = 32/6 = 16/3

Pages typed by Suresh in 1 hour = 40/5 = 8

Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3

Time taken to type 110 pages when Anil and Suresh work together = 110 × 3 /40 = 33/4

= 8 1/4 hours = 8 hour 15 minutes

Discussion

14.	Kamal Will Complete Work In 20 Days. If Suresh Is 25% More Efficient Than Kamal, He Can Complete The Work In --- Days.
Answer» WORK done by KAMAL in 1 DAY = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 DAYS Work done by Kamal in 1 day = 1/20 Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16 => Suresh can complete the work in 16 days

14.

Kamal Will Complete Work In 20 Days. If Suresh Is 25% More Efficient Than Kamal, He Can Complete The Work In --- Days.

Answer»

WORK done by KAMAL in 1 DAY = 1/20

Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16

=> Suresh can complete the work in 16 DAYS

Work done by Kamal in 1 day = 1/20

Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16

=> Suresh can complete the work in 16 days

Discussion

15.	10 Men Can Complete A Work In 7 Days. But 10 Women Need 14 Days To Complete The Same Work. How Many Days Will 5 Men And 10 Women Need To Complete The Work ?
Answer» Work done by 10 MEN in 1 day = 1/7 Work done by 1 MAN in 1 day = (1/7)/10 = 1/70 Work done by 10 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/140 Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140) = 5/70 + 10/140 = 1/7 =&GT; 5 men and 10 women can COMPLETE the work in 7 days Work done by 10 men in 1 day = 1/7 Work done by 1 man in 1 day = (1/7)/10 = 1/70 Work done by 10 women in 1 day = 1/14 Work done by 1 woman in 1 day = 1/140 Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140) = 5/70 + 10/140 = 1/7 => 5 men and 10 women can complete the work in 7 days

15.

10 Men Can Complete A Work In 7 Days. But 10 Women Need 14 Days To Complete The Same Work. How Many Days Will 5 Men And 10 Women Need To Complete The Work ?

Answer»

Work done by 10 MEN in 1 day = 1/7

Work done by 1 MAN in 1 day = (1/7)/10 = 1/70

Work done by 10 women in 1 day = 1/14

Work done by 1 woman in 1 day = 1/140

Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)

= 5/70 + 10/140 = 1/7

=&GT; 5 men and 10 women can COMPLETE the work in 7 days

Work done by 10 men in 1 day = 1/7

Work done by 1 man in 1 day = (1/7)/10 = 1/70

Work done by 10 women in 1 day = 1/14

Work done by 1 woman in 1 day = 1/140

Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)

= 5/70 + 10/140 = 1/7

=> 5 men and 10 women can complete the work in 7 days

Discussion

16.	P, Q And R Can Complete A Work In 24, 6 And 12 Days Respectively. The Work Will Be Completed In --- Days If All Of Them Are Working Together.
Answer» Work DONE by P in 1 DAY = 1/24 Work done by Q in 1 day = 1/6 Work done by R in 1 day = 1/12 Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24 =&GT; Working together, they will complete the work in 24/7 days = 3 3/7 days Work done by P in 1 day = 1/24 Work done by Q in 1 day = 1/6 Work done by R in 1 day = 1/12 Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24 => Working together, they will complete the work in 24/7 days = 3 3/7 days

16.

P, Q And R Can Complete A Work In 24, 6 And 12 Days Respectively. The Work Will Be Completed In --- Days If All Of Them Are Working Together.

Answer»

Work DONE by P in 1 DAY = 1/24

Work done by Q in 1 day = 1/6

Work done by R in 1 day = 1/12

Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24

=&GT; Working together, they will complete the work in 24/7 days = 3 3/7 days

Work done by P in 1 day = 1/24

Work done by Q in 1 day = 1/6

Work done by R in 1 day = 1/12

Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24

=> Working together, they will complete the work in 24/7 days = 3 3/7 days

Discussion

17.	P Is 30% More Efficient Than Q. P Can Complete A Work In 23 Days. If P And Q Work Together, How Much Time Will It Take To Complete The Same Work ?
Answer» Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 =&GT; q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 DAYS Work done by P in 1 day = 1/23 Let work done by Q in 1 day = q q × (130/100) = 1/23 => q = 100/(23×130) = 10/(23×13) Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13 => P and Q together can do the work in 13 days

17.

P Is 30% More Efficient Than Q. P Can Complete A Work In 23 Days. If P And Q Work Together, How Much Time Will It Take To Complete The Same Work ?

Answer»

Work done by P in 1 day = 1/23

Let work done by Q in 1 day = q

q × (130/100) = 1/23

=&GT; q = 100/(23×130) = 10/(23×13)

Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13

=> P and Q together can do the work in 13 DAYS

Work done by P in 1 day = 1/23

Let work done by Q in 1 day = q

q × (130/100) = 1/23

=> q = 100/(23×130) = 10/(23×13)

Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13

=> P and Q together can do the work in 13 days

Discussion

18.	A Can Complete A Work In 12 Days With A Working Of 8 Hours Per Day. B Can Complete The Same Work In 8 Days When Working 10 Hours A Day. If A And B Work Together, Working 8 Hours A Day, The Work Can Be Completed In --- Days.
Answer» A can complete the work in 12 DAYS working 8 hours a day => Number of hours A can complete the work = 12×8 = 96 hours => Work done by A in 1 hour = 1/96 B can complete the work in 8 days working 10 hours a day => Number of hours B can complete the work = 8×10 = 80 hours => Work done by B in 1 hour = 1/80 Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480 => A and B can complete the work in 480/11 hours A and B WORKS 8 hours a day Hence total days to complete the work with A and B working TOGETHER = (480/11)/ (8) = 60/11 days = 5 5/11 days A can complete the work in 12 days working 8 hours a day => Number of hours A can complete the work = 12×8 = 96 hours => Work done by A in 1 hour = 1/96 B can complete the work in 8 days working 10 hours a day => Number of hours B can complete the work = 8×10 = 80 hours => Work done by B in 1 hour = 1/80 Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480 => A and B can complete the work in 480/11 hours A and B works 8 hours a day Hence total days to complete the work with A and B working together = (480/11)/ (8) = 60/11 days = 5 5/11 days

18.

A Can Complete A Work In 12 Days With A Working Of 8 Hours Per Day. B Can Complete The Same Work In 8 Days When Working 10 Hours A Day. If A And B Work Together, Working 8 Hours A Day, The Work Can Be Completed In --- Days.

Answer»

A can complete the work in 12 DAYS working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours

=> Work done by A in 1 hour = 1/96

B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours

=> Work done by B in 1 hour = 1/80

Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480

=> A and B can complete the work in 480/11 hours

A and B WORKS 8 hours a day

Hence total days to complete the work with A and B working TOGETHER

= (480/11)/ (8) = 60/11 days = 5 5/11 days

A can complete the work in 12 days working 8 hours a day

=> Number of hours A can complete the work = 12×8 = 96 hours

=> Work done by A in 1 hour = 1/96

B can complete the work in 8 days working 10 hours a day

=> Number of hours B can complete the work = 8×10 = 80 hours

=> Work done by B in 1 hour = 1/80

Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480

=> A and B can complete the work in 480/11 hours

A and B works 8 hours a day

Hence total days to complete the work with A and B working together

= (480/11)/ (8) = 60/11 days = 5 5/11 days

Discussion

19.	A And B Can Finish A Work 30 Days If They Work Together. They Worked Together For 20 Days And Then B Left. A Finished The Remaining Work In Another 20 Days. In How Many Days A Alone Can Finish The Work ?
Answer» Amount of WORK DONE by A and B in 1 day = 1/30 Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3 Remaining work – 1 – 2/3 = 1/3 A completes 1/3 work in 20 days Amount of work A can do in 1 day = (1/3)/20 = 1/60 => A can COMPLETE the work in 60 days Amount of work done by A and B in 1 day = 1/30 Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3 Remaining work – 1 – 2/3 = 1/3 A completes 1/3 work in 20 days Amount of work A can do in 1 day = (1/3)/20 = 1/60 => A can complete the work in 60 days

19.

A And B Can Finish A Work 30 Days If They Work Together. They Worked Together For 20 Days And Then B Left. A Finished The Remaining Work In Another 20 Days. In How Many Days A Alone Can Finish The Work ?

Answer»

Amount of WORK DONE by A and B in 1 day = 1/30

Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3

Remaining work – 1 – 2/3 = 1/3

A completes 1/3 work in 20 days

Amount of work A can do in 1 day = (1/3)/20 = 1/60

=> A can COMPLETE the work in 60 days

Amount of work done by A and B in 1 day = 1/30

Amount of work done by A and B in 20 days = 20 × (1/30) = 20/30 = 2/3

Remaining work – 1 – 2/3 = 1/3

A completes 1/3 work in 20 days

Amount of work A can do in 1 day = (1/3)/20 = 1/60

=> A can complete the work in 60 days

Discussion

20.	3 Men And 7 Women Can Complete A Work In 10 Days . But 4 Men And 6 Women Need 8 Days To Complete The Same Work . In How Many Days Will 10 Women Complete The Same Work ?
Answer» Work DONE by 4 men and 6 women in 1 day = 1/8 Work done by 3 men and 7 women in 1 day = 1/10 LET 1 man does m work in 1 day and 1 woman does W work in 1 day. The above equations can be written as 4m + 6w = 1/8 ---(1) 3m + 7w = 1/10 ---(2) Solving equation (1) and (2) , we get m=11/400 and w=1/400 Amount of work 10 women can do in a day = 10 × (1/400) = 1/40 IE, 10 women can complete the work in 40 days Work done by 4 men and 6 women in 1 day = 1/8 Work done by 3 men and 7 women in 1 day = 1/10 Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as 4m + 6w = 1/8 ---(1) 3m + 7w = 1/10 ---(2) Solving equation (1) and (2) , we get m=11/400 and w=1/400 Amount of work 10 women can do in a day = 10 × (1/400) = 1/40 Ie, 10 women can complete the work in 40 days

20.

3 Men And 7 Women Can Complete A Work In 10 Days . But 4 Men And 6 Women Need 8 Days To Complete The Same Work . In How Many Days Will 10 Women Complete The Same Work ?

Answer»

Work DONE by 4 men and 6 women in 1 day = 1/8

Work done by 3 men and 7 women in 1 day = 1/10

LET 1 man does m work in 1 day and 1 woman does W work in 1 day. The above equations can be written as

4m + 6w = 1/8 ---(1)

3m + 7w = 1/10 ---(2)

Solving equation (1) and (2) , we get m=11/400 and w=1/400

Amount of work 10 women can do in a day = 10 × (1/400) = 1/40

IE, 10 women can complete the work in 40 days

Work done by 4 men and 6 women in 1 day = 1/8

Work done by 3 men and 7 women in 1 day = 1/10

Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as

4m + 6w = 1/8 ---(1)

3m + 7w = 1/10 ---(2)

Solving equation (1) and (2) , we get m=11/400 and w=1/400

Amount of work 10 women can do in a day = 10 × (1/400) = 1/40

Ie, 10 women can complete the work in 40 days

Discussion

21.	P Can Finish A Work In 18 Days. Q Can Finish The Same Work In 15 Days. Q Worked For 10 Days And Left The Job. How Many Days Does P Alone Need To Finish The Remaining Work ?
Answer» <P>Work DONE by P in 1 day = 1/18 Work done by Q in 1 day = 1/15 Work done by Q in 10 days = 10/15 = 2/3 Remaining work = 1 – 2/3 = 1/3 Number of days in which P can FINISH the remaining work = (1/3) / (1/18) = 6 Work done by P in 1 day = 1/18 Work done by Q in 1 day = 1/15 Work done by Q in 10 days = 10/15 = 2/3 Remaining work = 1 – 2/3 = 1/3 Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

21.

P Can Finish A Work In 18 Days. Q Can Finish The Same Work In 15 Days. Q Worked For 10 Days And Left The Job. How Many Days Does P Alone Need To Finish The Remaining Work ?

Answer»

<P>Work DONE by P in 1 day = 1/18

Work done by Q in 1 day = 1/15

Work done by Q in 10 days = 10/15 = 2/3

Remaining work = 1 – 2/3 = 1/3

Number of days in which P can FINISH the remaining work = (1/3) / (1/18) = 6

Work done by P in 1 day = 1/18

Work done by Q in 1 day = 1/15

Work done by Q in 10 days = 10/15 = 2/3

Remaining work = 1 – 2/3 = 1/3

Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

Discussion

22.	Machine P Can Print One Lakh Books In 8 Hours. Machine Q Can Print The Same Number Of Books In 10 Hours While Machine R Can Print The Same In 12 Hours. All The Machines Started Printing At 9 A.m. Machine P Is Stopped At 11 A.m. And The Remaining Two Machines Complete Work. Approximately At What Time Will The Printing Of One Lakh Books Be Completed ?
Answer» <P>WORK done by P in 1 hour = 1/8 Work done by Q in 1 hour = 1/10 Work done by R in 1 hour = 1/12 Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120 Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60 From 9 am to 11 am, all the machines were OPERATING. Ie, they all operated for 2 hours and work COMPLETED = 2 × (37/120) = 37/60 Pending work = 1- 37/60 = 23/60 Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm Work done by P in 1 hour = 1/8 Work done by Q in 1 hour = 1/10 Work done by R in 1 hour = 1/12 Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120 Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60 From 9 am to 11 am, all the machines were operating. Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60 Pending work = 1- 37/60 = 23/60 Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm

22.

Machine P Can Print One Lakh Books In 8 Hours. Machine Q Can Print The Same Number Of Books In 10 Hours While Machine R Can Print The Same In 12 Hours. All The Machines Started Printing At 9 A.m. Machine P Is Stopped At 11 A.m. And The Remaining Two Machines Complete Work. Approximately At What Time Will The Printing Of One Lakh Books Be Completed ?

Answer»

<P>WORK done by P in 1 hour = 1/8

Work done by Q in 1 hour = 1/10

Work done by R in 1 hour = 1/12

Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120

Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60

From 9 am to 11 am, all the machines were OPERATING.

Ie, they all operated for 2 hours and work COMPLETED = 2 × (37/120) = 37/60

Pending work = 1- 37/60 = 23/60

Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm

Work done by P in 1 hour = 1/8

Work done by Q in 1 hour = 1/10

Work done by R in 1 hour = 1/12

Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120

Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60

From 9 am to 11 am, all the machines were operating.

Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60

Pending work = 1- 37/60 = 23/60

Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11 which is approximately equal to 2 Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm

Discussion

23.	A Completes 80% Of A Work In 20 Days. Then B Also Joins And A And B Together Finish The Remaining Work In 3 Days. How Long Does It Need For B If He Alone Completes The Work?
Answer» WORK done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 DAY = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 =&GT; B can complete the work in 75/2 days = 37 1/2 days Work done by A in 20 days = 80/100 = 8/10 = 4/5 Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1) Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B) Work done by A and B in 1 day = 1/15 ---(2) Work done by B in 1 day = 1/15 – 1/25 = 2/75 => B can complete the work in 75/2 days = 37 1/2 days

23.

A Completes 80% Of A Work In 20 Days. Then B Also Joins And A And B Together Finish The Remaining Work In 3 Days. How Long Does It Need For B If He Alone Completes The Work?

Answer»

WORK done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 DAY = (4/5) / 20 = 4/100 = 1/25 --- (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 ---(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=&GT; B can complete the work in 75/2 days = 37 1/2 days

Work done by A in 20 days = 80/100 = 8/10 = 4/5

Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)

Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)

Work done by A and B in 1 day = 1/15 ---(2)

Work done by B in 1 day = 1/15 – 1/25 = 2/75

=> B can complete the work in 75/2 days = 37 1/2 days

Discussion

24.	P Can Do A Work In The Same Time In Which Q And R Together Can Do It. If P And Q Work Together, The Work Can Be Completed In 10 Days. R Alone Needs 50 Days To Complete The Same Work. Then Q Alone Can Do It In
Answer» WORK done by P and Q in 1 day = 1/10 Work done by R in 1 day = 1/50 Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50 But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 6/50 =&GT; Work done by P in 1 day = 3/50 => Work done by Q and R in 1 day = 3/50 Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25 So Q alone can do the work in 25 days. Work done by P and Q in 1 day = 1/10 Work done by R in 1 day = 1/50 Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50 But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 6/50 => Work done by P in 1 day = 3/50 => Work done by Q and R in 1 day = 3/50 Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25 So Q alone can do the work in 25 days.

24.

P Can Do A Work In The Same Time In Which Q And R Together Can Do It. If P And Q Work Together, The Work Can Be Completed In 10 Days. R Alone Needs 50 Days To Complete The Same Work. Then Q Alone Can Do It In

Answer»

WORK done by P and Q in 1 day = 1/10

Work done by R in 1 day = 1/50

Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50

But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as

Work done by P in 1 day × 2 = 6/50

=&GT; Work done by P in 1 day = 3/50

=> Work done by Q and R in 1 day = 3/50

Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25

So Q alone can do the work in 25 days.

Work done by P and Q in 1 day = 1/10

Work done by R in 1 day = 1/50

Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50

But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as

Work done by P in 1 day × 2 = 6/50

=> Work done by P in 1 day = 3/50

=> Work done by Q and R in 1 day = 3/50

Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25

So Q alone can do the work in 25 days.

Discussion

25.	A Can Do A Piece Of Work In 4 Hours . A And C Together Can Do It In Just 2 Hours, While B And C Together Need 3 Hours To Finish The Same Work. B Alone Can Complete The Work In --- Hours.
Answer» Work DONE by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12 Work done by B in 1 hour = 7/12 – 1/2 = 1/12 =&GT; B alone can COMPLETE the work in 12 hours. Work done by A in 1 hour = 1/4 Work done by B and C in 1 hour = 1/3 Work done by A and C in 1 hour = 1/2 Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12 Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours.

25.

A Can Do A Piece Of Work In 4 Hours . A And C Together Can Do It In Just 2 Hours, While B And C Together Need 3 Hours To Finish The Same Work. B Alone Can Complete The Work In --- Hours.

Answer»

Work DONE by A in 1 hour = 1/4

Work done by B and C in 1 hour = 1/3

Work done by A and C in 1 hour = 1/2

Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12

Work done by B in 1 hour = 7/12 – 1/2 = 1/12 =&GT; B alone can COMPLETE the work in 12 hours.

Work done by A in 1 hour = 1/4

Work done by B and C in 1 hour = 1/3

Work done by A and C in 1 hour = 1/2

Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12

Work done by B in 1 hour = 7/12 – 1/2 = 1/12 => B alone can complete the work in 12 hours.

Discussion

26.	6 Men And 8 Women Can Complete A Work In 10 Days. 26 Men And 48 Women Can Finish The Same Work In 2 Days. 15 Men And 20 Women Can Do The Same Work In - Days.
Answer» Let work done by 1 MAN in 1 day = m and work done by 1 woman in 1 day = b Work done by 6 men and 8 women in 1 day = 1/10 => 6m + 8b = 1/10 => 60m + 80b = 1 --- (1) Work done by 26 men and 48 women in 1 day = 1/2 => 26m + 48B = ½ => 52m + 96b = 1--- (2) Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200 Work done by 15 men and 20 women in 1 day = 15/100 + 20/200 =1/4 => TIME taken by 15 men and 20 women in doing the work = 4 DAYS Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b Work done by 6 men and 8 women in 1 day = 1/10 => 6m + 8b = 1/10 => 60m + 80b = 1 --- (1) Work done by 26 men and 48 women in 1 day = 1/2 => 26m + 48b = ½ => 52m + 96b = 1--- (2) Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200 Work done by 15 men and 20 women in 1 day = 15/100 + 20/200 =1/4 => Time taken by 15 men and 20 women in doing the work = 4 days

26.

6 Men And 8 Women Can Complete A Work In 10 Days. 26 Men And 48 Women Can Finish The Same Work In 2 Days. 15 Men And 20 Women Can Do The Same Work In - Days.

Answer»

Let work done by 1 MAN in 1 day = m and work done by 1 woman in 1 day = b

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8b = 1/10

=> 60m + 80b = 1 --- (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48B = ½

=> 52m + 96b = 1--- (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> TIME taken by 15 men and 20 women in doing the work = 4 DAYS

Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b

Work done by 6 men and 8 women in 1 day = 1/10

=> 6m + 8b = 1/10

=> 60m + 80b = 1 --- (1)

Work done by 26 men and 48 women in 1 day = 1/2

=> 26m + 48b = ½

=> 52m + 96b = 1--- (2)

Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200

Work done by 15 men and 20 women in 1 day

= 15/100 + 20/200 =1/4

=> Time taken by 15 men and 20 women in doing the work = 4 days

Discussion

27.	A Can Do A Particular Work In 6 Days . B Can Do The Same Work In 8 Days. A And B Signed To Do It For Rs. 3200. They Completed The Work In 3 Days With The Help Of C. How Much Is To Be Paid To C ?
Answer» AMOUNT of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400 Amount of work A can do in 1 day = 1/6 Amount of work B can do in 1 day = 1/8 Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24 Amount of work A + B + C can do = 1/3 Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24 work A can do in 1 day: work B can do in 1 day: work C can do in 1 day = 1/6 : 1/8 : 1/24 = 4 : 3 : 1 Amount to be paid to C = 3200 × (1/8) = 400

27.

A Can Do A Particular Work In 6 Days . B Can Do The Same Work In 8 Days. A And B Signed To Do It For Rs. 3200. They Completed The Work In 3 Days With The Help Of C. How Much Is To Be Paid To C ?

Answer»

AMOUNT of work A can do in 1 day = 1/6

Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day

= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400

Amount of work A can do in 1 day = 1/6

Amount of work B can do in 1 day = 1/8

Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24

Amount of work A + B + C can do = 1/3

Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24

work A can do in 1 day: work B can do in 1 day: work C can do in 1 day

= 1/6 : 1/8 : 1/24 = 4 : 3 : 1

Amount to be paid to C = 3200 × (1/8) = 400

Discussion

28.	A Is Thrice As Good As B In Work. A Is Able To Finish A Job In 60 Days Less Than B. They Can Finish The Work In - Days If They Work Together.
Answer» If A completes a work in 1 day, B completes the same work in 3 days Hence, if the difference is 2 days, B can complete the work in 3 days =&GT; if the difference is 60 days, B can complete the work in 90 days => AMOUNT of work B can do in 1 day= 1/90 Amount of work A can do in 1 day = 3 × (1/90) = 1/30 Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45 => A and B together can do the work in 45/2 days = 221/2 days If A completes a work in 1 day, B completes the same work in 3 days Hence, if the difference is 2 days, B can complete the work in 3 days => if the difference is 60 days, B can complete the work in 90 days => Amount of work B can do in 1 day= 1/90 Amount of work A can do in 1 day = 3 × (1/90) = 1/30 Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45 => A and B together can do the work in 45/2 days = 221/2 days

28.

A Is Thrice As Good As B In Work. A Is Able To Finish A Job In 60 Days Less Than B. They Can Finish The Work In - Days If They Work Together.

Answer»

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=&GT; if the difference is 60 days, B can complete the work in 90 days

=> AMOUNT of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 221/2 days

If A completes a work in 1 day, B completes the same work in 3 days

Hence, if the difference is 2 days, B can complete the work in 3 days

=> if the difference is 60 days, B can complete the work in 90 days

=> Amount of work B can do in 1 day= 1/90

Amount of work A can do in 1 day = 3 × (1/90) = 1/30

Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45

=> A and B together can do the work in 45/2 days = 221/2 days

Discussion

29.	P, Q And R Can Do A Work In 20, 30 And 60 Days Respectively. How Many Days Does It Need To Complete The Work If P Does The Work And He Is Assisted By Q And R On Every Third Day?
Answer» AMOUNT of work P can do in 1 day = 1/20 Amount of work Q can do in 1 day = 1/30 Amount of work R can do in 1 day = 1/60 P is WORKING ALONE and every third day Q and R is helping him Work completed in every THREE days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5 So work completed in 15 days = 5 × 1/5 = 1 IE, the work will be done in 15 days Amount of work P can do in 1 day = 1/20 Amount of work Q can do in 1 day = 1/30 Amount of work R can do in 1 day = 1/60 P is working alone and every third day Q and R is helping him Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5 So work completed in 15 days = 5 × 1/5 = 1 Ie, the work will be done in 15 days

29.

P, Q And R Can Do A Work In 20, 30 And 60 Days Respectively. How Many Days Does It Need To Complete The Work If P Does The Work And He Is Assisted By Q And R On Every Third Day?

Answer»

AMOUNT of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is WORKING ALONE and every third day Q and R is helping him

Work completed in every THREE days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

IE, the work will be done in 15 days

Amount of work P can do in 1 day = 1/20

Amount of work Q can do in 1 day = 1/30

Amount of work R can do in 1 day = 1/60

P is working alone and every third day Q and R is helping him

Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5

So work completed in 15 days = 5 × 1/5 = 1

Ie, the work will be done in 15 days

Discussion

30.	P Can Lay Railway Track Between Two Stations In 16 Days. Q Can Do The Same Job In 12 Days. With The Help Of R, They Completes The Job In 4 Days. How Much Days Does It Take For R Alone To Complete The Work ?
Answer» <P>AMOUNT of WORK P can do in 1 day = 1/16 Amount of work Q can do in 1 day = 1/12 Amount of work P, Q and R can TOGETHER do in 1 day = 1/4 Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48 => HENCE R can do the job on 48/5 days = 9 (3/5) days Amount of work P can do in 1 day = 1/16 Amount of work Q can do in 1 day = 1/12 Amount of work P, Q and R can together do in 1 day = 1/4 Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48 => Hence R can do the job on 48/5 days = 9 (3/5) days

30.

P Can Lay Railway Track Between Two Stations In 16 Days. Q Can Do The Same Job In 12 Days. With The Help Of R, They Completes The Job In 4 Days. How Much Days Does It Take For R Alone To Complete The Work ?

Answer»

<P>AMOUNT of WORK P can do in 1 day = 1/16

Amount of work Q can do in 1 day = 1/12

Amount of work P, Q and R can TOGETHER do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> HENCE R can do the job on 48/5 days = 9 (3/5) days

Amount of work P can do in 1 day = 1/16

Amount of work Q can do in 1 day = 1/12

Amount of work P, Q and R can together do in 1 day = 1/4

Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48

=> Hence R can do the job on 48/5 days = 9 (3/5) days

Discussion

31.	P Is Able To Do A Piece Of Work In 15 Days And Q Can Do The Same Work In 20 Days. If They Can Work Together For 4 Days, What Is The Fraction Of Work Left ?
Answer» <P>Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 FRACTION of work left = 1 – 7/15= 8/15 Amount of work P can do in 1 day = 1/15 Amount of work Q can do in 1 day = 1/20 Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60 Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15 Fraction of work left = 1 – 7/15= 8/15

31.

P Is Able To Do A Piece Of Work In 15 Days And Q Can Do The Same Work In 20 Days. If They Can Work Together For 4 Days, What Is The Fraction Of Work Left ?

Answer»

<P>Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

FRACTION of work left = 1 – 7/15= 8/15

Amount of work P can do in 1 day = 1/15

Amount of work Q can do in 1 day = 1/20

Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60

Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15

Fraction of work left = 1 – 7/15= 8/15

Discussion

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