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1.

If Vinit can do \(\frac{1}{4}\)th of a work in 3 days and Viraj can do \(\frac{1}{6}\)th of the same work in 4 days, how much will Viraj get if both work together and are paid Rs. 360 in all?1). Rs. 2402). Rs. 1203). Rs. 804). Rs. 360

Answer»

Since, vinit does 1/4 TH of the work in 3 days, he requires 12 days to complete the entire job.

Since, viraj does 1/6 th of the work in 4 days, he requires 24 days to complete the entire job.

∴ the rates of doing work for Vinit and Viraj are 1/12 and 1/24 respectively.

∴ Vinit and Viraj do the work in the ratio of 2 : 1 in TERMS of rate.

∴ they will be paid according to this ratio.

Let the common MULTIPLE be ‘x’

∴ the PAYMENTS of Vinit and Viraj will be 2x and x respectively.

∴ x + 2x = 360

∴ x = 120

∴ Viraj will be paid rupees = x = 120
Discussion
2.

1). 1 hr. 3 min.2). 1 hr. 18 min.3). 1 hr. 24 min.4). 1 hr. 42 min.

Answer»

Part filled by PIPES A & B in 1 hr = 1/4

Part emptied by pipe C in 1 hr = 1/10

Part emptied by pipe D in 1 hr = 1/12

Now, pipe A & B were open for = 3 hours

Pipe C was open for = 3 - 1 = 2 hours

Let pipe D was opened after ‘X’ hours of opening of pipe C,

Pipe D was open for = (2 - x) hours

Hence, part filled in 3 hours = 1/2

⇒ Part filled by A & B - Part emptied by C & D = 1/2

⇒ 3 × (1/4) - 2 × (1/10) - (2 - x) × (1/12) = 1/2

⇒ 3/4 - 1/5 - (2 - x)/12 = 1/2

⇒ 45 - 12 - 10 + 5x = 30

⇒ 5x = 7

⇒ x = 7/5 = 1.4 HRS = 1 hr. 24 min.

∴ Pipe D was opened after 1 hr. 24 min. of opening of pipe C
Discussion
3.

There are two pipes in a tank. Pipe A is for filling the tank and Pipe B is for emptying the tank. If A can fill the tank in 15 hours and B can empty the tank in 20 hours then find how many hours will it take to completely fill a half empty tank?1). 452). 403). 304). 35

Answer»

⇒ Work done by A in 1 hour = 1/15

⇒ Work done by B in 1 hour = - 1/20

⇒ Total work done by A and B in 1 hour = 1/15 + (- 1/20) = 1/15 – 1/20 = 1/60

⇒ They will FILL the full tank in 60 HOURS

∴ HALF tank can be fill in 30 hours
Discussion
4.

There are two cylindrical shaped tanks, P and Q. P has a capacity twice of Q. When tank P is filled at the rate of 2 liters per minute, it takes 20 minutes more to fill as compared to the time taken when tank Q is filled at 3 liters per minute. Find the capacity of tank Q.1). 30 liters2). 60 liters3). 120 liters4). 90 liters

Answer»

P has a capacity twice of Q.

Let us suppose that capacities of tanks P and Q are 2T liters and T liters, respectively.

When tank P is filled at the rate of 2 liters per minute, it takes 20 minutes to fill more as COMPARED to the TIME TAKEN when tank Q is filled at 3 liters per minute.

⇒ Time taken to fill tank P at 2 liters per minute = 2T/2 = T minutes

⇒ Time taken to fill tank Q at 3 liters per minute = T/3 minutes

T = 20 + (T/3)

⇒ 2T/3 = 20

⇒ T = 30

∴ Capacity of tank Q is 30 liters.
Discussion
5.

Quantity B: P & Q working alone can complete a wok in 20 and 30 days respectively. They started together but after 9 days P left, in how many days will the total work be completed?1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B

Answer»

Quantity A:

Let total UNITS of WORK = 60 units (LCM of 10, 12 and 20)

∴ Efficiency of A and B together = 60/10 = 6

Efficiency of B and C together = 60/12 = 5

Efficiency of C and A together = 60/20 = 3

∴ Efficiency of A, B and C together = (6 + 5 + 3)/2 = 7

∴ Efficiency of B = 7 – 3 = 4

∴ Time taken by B to finish the work alone = 60/4 = 15 days

Quantity B:

Let total units of work = 60 units (LCM of 20 and 30)

∴ Efficiency of P = 60/20 = 3

Efficiency of Q = 60/30 = 2

Since P left after 9 days;

Unit of work left after 9 days = 60 – 9 × (3 + 2) = 15 units

∴ Time taken by Q to finish the remaining work = 15/2 = 7.5 days

∴ Total time to finish the work = 9 + 7.5 = 16.5 days

∴ Quantity B > Quantity A
Discussion
6.

Quantity B: A alone can paint a building in 15 days and B can do the same work in 20 days. Both were jointly hired to do the work for Rs. 6000. After 3 days B left and C joined who performed 1/3 of the remaining work. Calculate the wage of A.1). Quantity A > Quantity B2). Quantity A < Quantity B3). Quantity A ≥ Quantity B4). Quantity A ≤ Quantity B

Answer»

Quantity A:

Let the rent for 1 month for 1 cow be Rs. x

⇒ Rent of A = 9 × 8 × x = 72X

⇒ Rent of B = 10 × 5 × x = 50x

⇒ Rent of C = 14 × 10 × x = 140x

⇒ Rent of D = 7 × 9 × x = 63X

A's share = Rs.720

⇒ 72x = 720

⇒ x = 10

⇒ Total rent of the pasture = 72x + 50x + 140x + 63x = 325x

⇒ 325x = 325 × 10 = Rs. 3250

Quantity B:

⇒ A’s income per day = 6000/15 = 400

⇒ B’s income per day = 6000/20 = 300

⇒ A’s income in 3 days = 400 × 3 = 1200

⇒ B’s income in 3 days = 300 × 3 = 900

Now, B doesn’t work further but A still have done 2/3 of the remaining work.

⇒ Amount LEFT for remaining work = 6000 – 1200 – 900 = 3900

⇒ Amount A will get = (2/3) × 3900 = 2 × 1300 = 2600

⇒ Amount C will get = (1/3) × 3900 = 1 × 1300 = 1300

⇒ A’s total income = 1200 + 2600 = 3800

⇒ The income of A is Rs. 3800

∴ Quantity A < Quantity B
Discussion