200 + Interview Questions in Ratio and Proportion in Quantitative Aptitude Page 1 InterviewSolution

1.	At present, father age is two times of his son's age. And son's age is 30 years. Find the ratio of age of son and father after 3 years.1. 21 : 222. 11 : 213. 17 : 194. 17 : 20
Answer» Correct Answer - Option 2 : 11 : 21 Given Son's age = 30 years Father's age = 2(son's age) Calculation Father's present age = 2 × 30 = 60 years Son's age after 3 years = 30 + 3 = 33 years Father's age after 3 years = 60 + 3 = 63 years Ratio of their age after 3 years = 33 : 63 = 11 : 21 ∴The ratio of age of son to that of father after 3 years is 11 : 21

1.

At present, father age is two times of his son's age. And son's age is 30 years. Find the ratio of age of son and father after 3 years.1. 21 : 222. 11 : 213. 17 : 194. 17 : 20

Answer» Correct Answer - Option 2 : 11 : 21

Given

Son's age = 30 years

Father's age = 2(son's age)

Calculation

Father's present age = 2 × 30

= 60 years

Son's age after 3 years = 30 + 3

= 33 years

Father's age after 3 years = 60 + 3

= 63 years

Ratio of their age after 3 years = 33 : 63 = 11 : 21

∴The ratio of age of son to that of father after 3 years is 11 : 21

Discussion

2.	If a ∶ b = 3 ∶ 2, b ∶ c = 5 ∶ 7 and d ∶ c = 3 ∶ 4. Then find a ∶ b ∶ c ∶ d.1. 17 ∶ 20 ∶ 28 ∶ 132. 28 ∶ 20 ∶ 22 ∶ 213. 30 ∶ 20 ∶ 28 ∶ 214. 30 ∶ 25 ∶ 28 ∶ 27
Answer» Correct Answer - Option 3 : 30 ∶ 20 ∶ 28 ∶ 21 Given: a ∶ b = 3 ∶ 2 b ∶ c = 5 ∶ 7 c ∶ d = 4∶ 3 Calculation: a ∶ b ∶ c ∶ d 3 ∶ 2 ∶ 2 ∶ 2 5 ∶ 5 ∶ 7 ∶ 7 4 ∶ 4 ∶ 4 ∶ 3 ⇒ (3 × 5 × 4) ∶ (2 × 5 × 4) ∶ (2 × 7 × 4) ∶(2 × 7 × 3) ⇒ 60 ∶ 40 ∶ 56 ∶ 42 ⇒ 30 ∶ 20 ∶ 28 ∶ 21 ∴ a ∶ b ∶ c ∶ d =30 ∶ 20 ∶ 28 ∶ 21 The correct option is 3 i.e.30 ∶ 20 ∶ 28 ∶ 21

2.

If a ∶ b = 3 ∶ 2, b ∶ c = 5 ∶ 7 and d ∶ c = 3 ∶ 4. Then find a ∶ b ∶ c ∶ d.1. 17 ∶ 20 ∶ 28 ∶ 132. 28 ∶ 20 ∶ 22 ∶ 213. 30 ∶ 20 ∶ 28 ∶ 214. 30 ∶ 25 ∶ 28 ∶ 27

Answer» Correct Answer - Option 3 : 30 ∶ 20 ∶ 28 ∶ 21

Given:

a ∶ b = 3 ∶ 2

b ∶ c = 5 ∶ 7

c ∶ d = 4∶ 3

Calculation:

a ∶ b ∶ c ∶ d

3 ∶ 2 ∶ 2 ∶ 2

5 ∶ 5 ∶ 7 ∶ 7

4 ∶ 4 ∶ 4 ∶ 3

⇒ (3 × 5 × 4) ∶ (2 × 5 × 4) ∶ (2 × 7 × 4) ∶(2 × 7 × 3)

⇒ 60 ∶ 40 ∶ 56 ∶ 42

⇒ 30 ∶ 20 ∶ 28 ∶ 21

∴ a ∶ b ∶ c ∶ d =30 ∶ 20 ∶ 28 ∶ 21

The correct option is 3 i.e.30 ∶ 20 ∶ 28 ∶ 21

Discussion

3.	Five years ago,the ratio between the age of P and Q is 7 : 9 and the present age ratio is 4 : 5. Find the present age of Q.1. 40 years2. 50 years3. 30 years4. 25 years
Answer» Correct Answer - Option 2 : 50 years Given Ratio of present age of P and Q is 4 : 5 Calculation Let the present age of P and Q is 4x and 5x According to question (4x - 5)/(5x - 5) = 7/9 9(4x - 5) = 7(5x - 5) 36x - 45 = 35x - 35 x = - 35 + 45 x = 10 Present age of Q is 50 years[i.e. 5(10)]

3.

Five years ago,the ratio between the age of P and Q is 7 : 9 and the present age ratio is 4 : 5. Find the present age of Q.1. 40 years2. 50 years3. 30 years4. 25 years

Answer» Correct Answer - Option 2 : 50 years

Given

Ratio of present age of P and Q is 4 : 5

Calculation

Let the present age of P and Q is 4x and 5x

According to question

(4x - 5)/(5x - 5) = 7/9

9(4x - 5) = 7(5x - 5)

36x - 45 = 35x - 35

x = - 35 + 45

x = 10

Present age of Q is 50 years[i.e. 5(10)]

Discussion

4.	If Rs.1440/- are divided among A,B and C so that A receives 1/3rd as much as B and B receives 1/4th as much as C. The amount B received is:
Answer» Rs.270/- NA

4.

If Rs.1440/- are divided among A,B and C so that A receives 1/3rd as much as B and B receives 1/4th as much as C. The amount B received is:

Answer»

Rs.270/-

NA

Discussion

5.	In what proportion must rice at Rs 50 per kg be mixed with rice at Rs 70 per kg, so that the mixture be worth Rs 56 a kg ?
Answer» 7 : 3 Ratio = 14/6

5.

In what proportion must rice at Rs 50 per kg be mixed with rice at Rs 70 per kg, so that the mixture be worth Rs 56 a kg ?

Answer»

7 : 3

Ratio = 14/6

Discussion

6.	The ratio of A's age to B's is 5 : 9 . After 15 years, the new ratio of their ages will be 2 : 3. What is the age of A at present ?
Answer» 25 years A/B = 5/9 ∴ 9A = 5B .....(1) A + 15/B + 12 = 2/3 ∴ 2B - 3A = 15 ......(2) Solving EQN (1) and (2), we get A = 25 and B = 45

6.

The ratio of A's age to B's is 5 : 9 . After 15 years, the new ratio of their ages will be 2 : 3. What is the age of A at present ?

Answer»

25 years

A/B = 5/9
∴ 9A = 5B .....(1)
A + 15/B + 12 = 2/3
∴ 2B - 3A = 15 ......(2)
Solving EQN (1) and (2), we get A = 25 and B = 45

Discussion

7.	Ram, Rakesh and Vijay invested in the ratio of 3:5:6 in business. If the amount invested by Rakesh is Rs. 75000, what is the total amount invested in the business ?
Answer» Let the total AMOUNT be 3x + 5X + 6x Amount by Rakesh = 5x = 75,000 RS 5x = 75,000 x = 15,000 Total amount = 315,000 + 75,000 + 615,000 = 45,000 + 75,000 + 90,000 = 210,000 Rs = Rs 2.1 Lakh

7.

Ram, Rakesh and Vijay invested in the ratio of 3:5:6 in business. If the amount invested by Rakesh is Rs. 75000, what is the total amount invested in the business ?

Answer»

Let the total AMOUNT be 3x + 5X + 6x

Amount by Rakesh = 5x = 75,000 RS

5x = 75,000

x = 15,000

Total amount = 3*15,000 + 75,000 + 6*15,000

= 45,000 + 75,000 + 90,000

= 210,000 Rs

= Rs 2.1 Lakh

Discussion

8.	Two years ago the ratio of the ages of Swati and Khyati was 5 : 7 . Two years hence the ratio of their ages will be 7 : 9. What is the present age of Khyati ?
Answer» 16 years Suppose TWO years age Swati's age was 5x and two years age Khyati's age was 7x. So two years HENCE swati's age will be 5x + 4 and Khyati's age's will be 7x + 4. But, 5x + 4/7x + 4 = 7/9 = 45x + 36 = 49 x + 28= 4x = 8 ∴ x = 2 ∴ Two years age Khyati's age was 14 years. So, the present age of Khyati's is 16 years.

8.

Two years ago the ratio of the ages of Swati and Khyati was 5 : 7 . Two years hence the ratio of their ages will be 7 : 9. What is the present age of Khyati ?

Answer»

16 years

Suppose TWO years age Swati's age was 5x and two years age Khyati's age was 7x.
So two years HENCE swati's age will be 5x + 4 and Khyati's age's will be 7x + 4.
But, 5x + 4/7x + 4 = 7/9
= 45x + 36 = 49 x + 28= 4x = 8
∴ x = 2
∴ Two years age Khyati's age was 14 years.
So, the present age of Khyati's is 16 years.

Discussion

9.	A milkman adds 4 litres of water to 16 litres of milk and another 9 litres of water to 27 litres of milk. What will be the ratio of the fraction of milk in the two mixtures ?
Answer» 16 : 15 Fraction of MILK in the first mixture= 16/20 = 4/5 Fraction of milk in the second MIX = 27/36 = 3/4 Ratio of their STRENGTH = 16 : 15

9.

A milkman adds 4 litres of water to 16 litres of milk and another 9 litres of water to 27 litres of milk. What will be the ratio of the fraction of milk in the two mixtures ?

Answer»

16 : 15

Fraction of MILK in the first mixture= 16/20 = 4/5
Fraction of milk in the second MIX = 27/36 = 3/4
Ratio of their STRENGTH = 16 : 15

Discussion

10.	If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?
Answer» 810 acres 12 MEN

10.

If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?

Answer»

810 acres

12 MEN

Discussion

11.	Rita invested 25% more than Sunil. Sunil invested 30% less than Abhinav who invested Rs. 6,000. What is the respective ratio between the amount that Rita invested and the total amount invested by all
Answer» 35 : 103 Abhinav's INVESTMENT = Rs. 6000 Sunil's Investment = 70 X 6000/100= Rs. 4200 Rita's Investment = 4200 x 125/100= Rs. 5250 Therefore Required RATIO= 5250 : (6000 + 4200 + 5250) = 5250 : 15450 = 35 : 103

11.

Rita invested 25% more than Sunil. Sunil invested 30% less than Abhinav who invested Rs. 6,000. What is the respective ratio between the amount that Rita invested and the total amount invested by all

Answer»

35 : 103

Abhinav's INVESTMENT = Rs. 6000
Sunil's Investment = 70 X 6000/100= Rs. 4200
Rita's Investment = 4200 x 125/100= Rs. 5250
Therefore Required RATIO= 5250 : (6000 + 4200 + 5250)
= 5250 : 15450
= 35 : 103

Discussion

12.	125 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?
Answer» <P> 50 liters Milk = 3/5 * 125 = 75 liters Water = 50 liters 75 : (50+P) = 3:4 150 + 3P = 400 => P = 50 50 liters of water are to be ADDED for the RATIO become 3:4.

12.

125 liters of a mixture of milk and water contains in the ratio 3:2. How much water should now be added so that the ratio of milk and water becomes 3:4?

Answer»

<P> 50 liters

Milk = 3/5 * 125 = 75 liters
Water = 50 liters
75 : (50+P) = 3:4
150 + 3P = 400 => P = 50
50 liters of water are to be ADDED for the RATIO become 3:4.

Discussion

13.	Five kgs. of Masoor cost Rs. 135/- whereas eight kg. Chana cost Rs. 96/- What is the ratio of per kg. cost of Masoor to that of Chana?
Answer» 9 : 4 9 : 4

13.

Five kgs. of Masoor cost Rs. 135/- whereas eight kg. Chana cost Rs. 96/- What is the ratio of per kg. cost of Masoor to that of Chana?

Answer»

9 : 4

Discussion

14.	Akash, Ramesh and Kamlesh invest in a business in the ratio of 2 : 3 : 5. If the amount invested by Akash is Rs 12000, what is the total amount invested ?
Answer» Rs. 60,000 Total of the RATIO = 2 + 3 + 5 = 10 ∴ Total amt/10 X 2 = 12000 ∴ Total amount= 12000 x 10/2 = Rs 60000

14.

Akash, Ramesh and Kamlesh invest in a business in the ratio of 2 : 3 : 5. If the amount invested by Akash is Rs 12000, what is the total amount invested ?

Answer»

Rs. 60,000

Total of the RATIO = 2 + 3 + 5 = 10
∴ Total amt/10 X 2 = 12000
∴ Total amount= 12000 x 10/2 = Rs 60000

Discussion

15.	If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then A:B:C:D is:
Answer» 16:24:30:35 A:B = 2:3, B:C = 4:5 = (4 * 3/4):(5 * 3/4) = 3:15/4 and C:D = 6:7 = (6 * 15/24):(7 * 15/24) = 15/4:35/8 A:B:C:D = 2:3:15/4:35/8 = 16:24:30:35

15.

If A:B = 2:3, B:C = 4:5 and C:D = 6:7, then A:B:C:D is:

Answer»

16:24:30:35

A:B = 2:3, B:C = 4:5 = (4 * 3/4):(5 * 3/4) = 3:15/4

and C:D = 6:7 = (6 * 15/24):(7 * 15/24) = 15/4:35/8 A:B:C:D = 2:3:15/4:35/8 = 16:24:30:35

Discussion

16.	If a : b = 4 : 1, then find (a - 3b)/(2a - b).
Answer» 1/7 a : b = 4 : 1 a/b = 4/1 => a = 4b (a - 3B)/(2A - b) = (4b - 3b)/[2(4b) - b] = b/(8B - b) = b/7b => 1/7

16.

If a : b = 4 : 1, then find (a - 3b)/(2a - b).

Answer»

1/7

a : b = 4 : 1

a/b = 4/1 => a = 4b

(a - 3B)/(2A - b) = (4b - 3b)/[2(4b) - b]

= b/(8B - b) = b/7b => 1/7

Discussion

17.	Girish started a business investing Rs. 45,000. After 3 months, Vijay joined him with a capital of Rs. 60,000. After another 6 months, Ankush joined them with a capital of Rs. 90,000. Girish's share-
Answer» RS. 5500 Ratio of the EQUIVALENT CAPITALS of Gitish, Vijay nad Ankush for 1 month = 45000 x 12 : 9 x 60000 : 6 x 90000 = 45 x 12 : 9 x 60 : 6 x 90 = 1 : 1 : 1 ∴ Girish's share = Rs (1/3 x 16500) = Rs. 5500

17.

Girish started a business investing Rs. 45,000. After 3 months, Vijay joined him with a capital of Rs. 60,000. After another 6 months, Ankush joined them with a capital of Rs. 90,000. Girish's share-

Answer»

RS. 5500

Ratio of the EQUIVALENT CAPITALS of Gitish, Vijay nad Ankush for 1 month
= 45000 x 12 : 9 x 60000 : 6 x 90000
= 45 x 12 : 9 x 60 : 6 x 90
= 1 : 1 : 1
∴ Girish's share = Rs (1/3 x 16500) = Rs. 5500

Discussion

18.	15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
Answer» 18 Binders

18.

15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?

Answer»

18

Binders

Discussion

19.	A mixture contains milk and water in the ratio 7:3. On adding 20 liters of water, the ratio of milk to water becomes 7:5. Total quantity of milk & water before adding water to it?
Answer» 100 NA

19.

A mixture contains milk and water in the ratio 7:3. On adding 20 liters of water, the ratio of milk to water becomes 7:5. Total quantity of milk & water before adding water to it?

Answer»

100

NA

Discussion

20.	Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?
Answer» Rs.160/- NA

20.

Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:?

Answer»

Rs.160/-

NA

Discussion

21.	The first three terms of a proportion are 3, 9 and 12. The fourth term is?
Answer» 36 (9*12)/3 = 36

21.

The first three terms of a proportion are 3, 9 and 12. The fourth term is?

Answer»

36

(9*12)/3 = 36

Discussion

22.	1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
Answer» 12.5 100015 = 1200X x = 12.5

22.

1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?

Answer»

12.5

1000*15 = 1200*X

x = 12.5

Discussion

23.	A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?
Answer» 20cm 1: 2/5 = 5: 2 2/7 * 70 = 20

23.

A 70 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be?

Answer»

20cm

1: 2/5 = 5: 2

2/7 * 70 = 20

Discussion

24.	96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?
Answer» 42 X/7 = y/9 => x:y = 7:9 7/16 * 96 = 42

24.

96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal. Find the smallest part?

Answer»

42

X/7 = y/9 => x:y = 7:9

7/16 * 96 = 42

Discussion

25.	The triplicate ratio of 1 : 2 is?
Answer» C) 1:8 Answer: This question is based on ratio and proportion. TRIPLICATE ratio: triplicate is the ratio of cube of GIVEN TWO quantities a and b are given then triplicate is $a^3 : b^3.$ Here the question wants find triplicate of 1:2 according to above EXPLANATION,triplicate of given equation is $1^3 : 2^3 = 1 : 8 $ hence, answer is $1:8 $

25.

The triplicate ratio of 1 : 2 is?

Answer»

C) 1:8

Answer:

This question is based on ratio and proportion. TRIPLICATE ratio: triplicate is the ratio of cube of GIVEN TWO quantities a and b are given then triplicate is $a^3 : b^3.$

Here the question wants find triplicate of 1:2 according to above EXPLANATION,triplicate of given equation is $1^3 : 2^3 = 1 : 8 $

hence, answer is $1:8 $

Discussion

26.	The duplicate ratio of 3 : 4 is?
Answer» 9 : 16 32 : 42 = 9 :16

26.

The duplicate ratio of 3 : 4 is?

Answer»

9 : 16

32 : 42 = 9 :16

Discussion

27.	The inverse ratio of 3 : 2 : 1 is?
Answer» 2 : 3 : 6 1/3: 1/2: 1/1 = 2:3:6

27.

The inverse ratio of 3 : 2 : 1 is?

Answer»

2 : 3 : 6

1/3: 1/2: 1/1 = 2:3:6

Discussion

28.	The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife?
Answer» Cannot be determined Let the present ages of Anil and his SON be 7X and 3X years respectively. Let the present AGE of the son's mother be m years. (m + 6)/(3x + 6) = 2/1 m = 6X + 6 Ratio of the present ages of Anil and his son's mother = 7x/(6x + 6). This cannot be found uniquely.

28.

The ratio of the ages of Anil and his son at present is 7:3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2:1. Find the ratio of the present ages of Anil and his wife?

Answer»

Cannot be determined

Let the present ages of Anil and his SON be 7X and 3X years respectively.
Let the present AGE of the son's mother be m years.
(m + 6)/(3x + 6) = 2/1
m = 6X + 6
Ratio of the present ages of Anil and his son's mother = 7x/(6x + 6).
This cannot be found uniquely.

Discussion

29.	The ratio of the present ages of Ram and Shyam is 4 : 3. The ratio of their ages after 9 years will be 7 : 6 . What will be the ratio of their ages after 12 years ?
Answer» 8 : 7 Let the present age of Ram and SHYAM be 4x and 3X yrs. 4x + 9/3x + 9 = 7/6 Therefore, X = 3 Therefore, The ages of Ram and shyam are 12 and 9 years. Therefore, Required ratio = 12 + 12/9 + 12 = 24/21 = 8/7

29.

The ratio of the present ages of Ram and Shyam is 4 : 3. The ratio of their ages after 9 years will be 7 : 6 . What will be the ratio of their ages after 12 years ?

Answer»

8 : 7

Let the present age of Ram and SHYAM be 4x and 3X yrs.
4x + 9/3x + 9 = 7/6
Therefore, X = 3
Therefore, The ages of Ram and shyam are 12 and 9 years.
Therefore, Required ratio = 12 + 12/9 + 12 = 24/21 = 8/7

Discussion

30.	If an amount of Rs 90300 is distributed equally among 21 children, how much amount would each get ?
Answer» RS. 3225 Required AMOUNT = 90300/28

30.

If an amount of Rs 90300 is distributed equally among 21 children, how much amount would each get ?

Answer»

RS. 3225

Required AMOUNT = 90300/28

Discussion

31.	The ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his w
Answer» Cannot be determined Let the present ages of Anil and his SON be 7X and 3x years respectively. Let the present age of the son'smother be m years. (m + 6) / (3x + 6) = 2/1 m + 6 = 6x + 12 => m = 6x + 6 Ratio of the present ages of Anil and the son's mother = 7x / (6x + 6). This cannot be found UNIQUELY.

31.

The ratio of the ages of Anil and his son at present is 7 : 3. Six years hence, the ratio of the ages of the Anil's wife and the son will be 2 : 1. Find the ratio of the present ages of Anil and his w

Answer»

Cannot be determined

Let the present ages of Anil and his SON be 7X and 3x years respectively.

Let the present age of the son'smother be m years.

(m + 6) / (3x + 6) = 2/1

m + 6 = 6x + 12 => m = 6x + 6

Ratio of the present ages of Anil and the son's mother = 7x / (6x + 6).

This cannot be found UNIQUELY.

Discussion

32.	Supriya's monthly income is twice Deepa's monthly income. The ratio of the monthly income of Deepa and Sandhya is 7 : 3 respectively and their average monthly income is Rs 25,000. What is Supriya's mo
Answer» Rs. 70,000 Supriya : Deepa=2 : 1 = 14 : 7 Deepa : Sandhya = 7 : 3 ∴ Supriya : Deepa : Sandhya = 14 : 7 : 3 ∴ 7x + 3X = 2 x 25000 ∴ x = 5000 ∴ Supriya's monthly INCOME= 14 x 5000 = Rs. 70000

32.

Supriya's monthly income is twice Deepa's monthly income. The ratio of the monthly income of Deepa and Sandhya is 7 : 3 respectively and their average monthly income is Rs 25,000. What is Supriya's mo

Answer»

Rs. 70,000

Supriya : Deepa=2 : 1 = 14 : 7
Deepa : Sandhya = 7 : 3
∴ Supriya : Deepa : Sandhya = 14 : 7 : 3
∴ 7x + 3X = 2 x 25000
∴ x = 5000
∴ Supriya's monthly INCOME= 14 x 5000 = Rs. 70000

Discussion

33.	The length and breadth of a rectangle are in the ratio 3 : 1. If the breadth is 7 cm, then the length of the rectangle is:
Answer» 21 CM 21 cm

33.

The length and breadth of a rectangle are in the ratio 3 : 1. If the breadth is 7 cm, then the length of the rectangle is:

Answer»

21 CM

21 cm

Discussion

34.	If of Viren's salary is equal total of Amit's Salary their Amits salary.
Answer» Rs. 36000 Ratio of VIREN's and AMIT's income = 1/4 : 3/2 = 1 : 6 ∴ Amit's salary= Rs. (6/7 X 42000)

34.

If of Viren's salary is equal total of Amit's Salary their Amits salary.

Answer»

Rs. 36000

Ratio of VIREN's and AMIT's income
= 1/4 : 3/2 = 1 : 6
∴ Amit's salary= Rs. (6/7 X 42000)

Discussion

35.	If the product of the ages of A and B is 864 years and the ratio of their ages is 3 : 2, what is the age of 'B' ?
Answer» 24 years Age of B = 2 X √864/3x2 = 2 √864/6 = 2√144 = 2 x 12 = 24 YRS

35.

If the product of the ages of A and B is 864 years and the ratio of their ages is 3 : 2, what is the age of 'B' ?

Answer»

24 years

Age of B = 2 X √864/3x2 = 2 √864/6
= 2√144 = 2 x 12 = 24 YRS

Discussion

36.	Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings?
Answer» Rs.3600 Let the INCOME and the expenditure of the person be Rs.5x and Rs.4X respectively. Income, 5x = 18000 => x = 3600 SAVINGS = Income - expenditure = 5x - 4x = x So, savings = Rs.3600.

36.

Income and expenditure of a person are in the ratio 5:4. If the income of the person is Rs.18000, then find his savings?

Answer»

Rs.3600

Let the INCOME and the expenditure of the person be Rs.5x and Rs.4X respectively.
Income, 5x = 18000 => x = 3600
SAVINGS = Income - expenditure = 5x - 4x = x
So, savings = Rs.3600.

Discussion

37.	Ramesh has somehens and goats. If the total number of animal heads is 68 and the total number, of legs is 214, how many hens dose Ramesh have ?
Answer» 29 Let no. of HENS = X and GOATS = y Therefore, x + y = 68

37.

Ramesh has somehens and goats. If the total number of animal heads is 68 and the total number, of legs is 214, how many hens dose Ramesh have ?

Answer»

29

Let no. of HENS = X and GOATS = y
Therefore, x + y = 68

Discussion

38.	Three persons A, B and C divide a certain amount of money such that A's share is Rs. 4 less than half of the total amount, B's share is Rs. 8 more than half of what is left and finally C takes the res
Answer» 80 Let the TOTAL amount be Rs. p. Let shares of A and B be Rs. x and Rs. y respectively. C's share was Rs. 14 we have, x + y + 14 = p ----- (1) From the given DATA, x = (p/2) - 4 ----- (2) Remaining amount = p - (p/2 - 4) => p/2 + 4. y = 1/2(p/2 + 4) + 8 => p/4 + 10 ----- (3) From (1), (2) and (3) p/2 - 4 + p/4 + 10 + 14 = p 3p/4 + 20 = p p/4 = 20 => p = Rs. 80.

38.

Three persons A, B and C divide a certain amount of money such that A's share is Rs. 4 less than half of the total amount, B's share is Rs. 8 more than half of what is left and finally C takes the res

Answer»

80

Let the TOTAL amount be Rs. p.
Let shares of A and B be Rs. x and Rs. y respectively.
C's share was Rs. 14
we have, x + y + 14 = p ----- (1)
From the given DATA, x = (p/2) - 4 ----- (2)
Remaining amount = p - (p/2 - 4) => p/2 + 4.
y = 1/2(p/2 + 4) + 8 => p/4 + 10 ----- (3)
From (1), (2) and (3)
p/2 - 4 + p/4 + 10 + 14 = p
3p/4 + 20 = p
p/4 = 20 => p = Rs. 80.

Discussion

39.	The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest
Answer» 36 KG Let the weights of the three boys be 4k, 5k and 6k respectively. 4k + 6k = 5k + 45 => 5k = 45 => K = 9 Therefore the weight of the lightest BOY = 4k = 4(9) = 36 kg.

39.

The weights of three boys are in the ratio 4 : 5 : 6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest

Answer»

36 KG

Let the weights of the three boys be 4k, 5k and 6k respectively.

4k + 6k = 5k + 45

=> 5k = 45 => K = 9

Therefore the weight of the lightest BOY

= 4k = 4(9) = 36 kg.

Discussion

40.	The total number of students in a school is 5050. If the number of girls in the school is 2450, then what is the respective ratio of the total number of boys to the total number of girls in the school
Answer» 49 : 52 49 : 52

40.

The total number of students in a school is 5050. If the number of girls in the school is 2450, then what is the respective ratio of the total number of boys to the total number of girls in the school

Answer»

49 : 52

Discussion

41.	The ratio of income of A and B is 5:4 and their expenditure is as 3:2. If at the end of the year, each saves Rs. 800, then the income of A is
Answer» RS. 2000 Rs. 2000

41.

The ratio of income of A and B is 5:4 and their expenditure is as 3:2. If at the end of the year, each saves Rs. 800, then the income of A is

Answer»

RS. 2000

Rs. 2000

Discussion

42.	Narendra started a business, investing Rs 30,000. Six months later, Chandan joined him with Rs 15,000. If they make a profit of Rs 10,000 at the end of the year, what should be the share of Narendra ?
Answer» RS 8000 30000 x 12 : 15000 x 6 = 4 : 1 Because, NARENDRA's share = 44/5 x 10000 = Rs. 8000

42.

Narendra started a business, investing Rs 30,000. Six months later, Chandan joined him with Rs 15,000. If they make a profit of Rs 10,000 at the end of the year, what should be the share of Narendra ?

Answer»

RS 8000

30000 x 12 : 15000 x 6
= 4 : 1
Because, NARENDRA's share = 44/5 x 10000 = Rs. 8000

Discussion

43.	The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?
Answer» 3:2 Let the earnings of P and Q be 9x and 10X respectively. New RATIO = [9x + 1/4 (9x)]/[10x - 1/4 (10x)] => 9(1 + 1/4)/10(1 - 1/4) => 9/10 * (5/4)/(3/4) = 3/2

43.

The ratio of the earnings of P and Q is 9:10. If the earnings of P increases by one-fourth and the earnings of Q decreases by one-fourth, then find the new ratio of their earnings?

Answer»

3:2

Let the earnings of P and Q be 9x and 10X respectively.
New RATIO = [9x + 1/4 (9x)]/[10x - 1/4 (10x)]
=> 9*(1 + 1/4)/10*(1 - 1/4)
=> 9/10 * (5/4)/(3/4) = 3/2

Discussion

44.	The sub-duplicate ratio of 1:4 is
Answer» 1:2

44.

The sub-duplicate ratio of 1:4 is

Answer»

1:2

Discussion

45.	An amount of money is distributed among A, B and C in the ratio of 1:2:9. If C gives Rs. 400 from his share to B, the new ratio becomes 1 : 3 : 8 . What is the total amount ?
Answer» Rs. 4800 Let the amount received by A, B and C be x, 2X and 9X respectively. ∴ TOTAL = 12x x : 2x + 400 : 9x - 400 = 1 : 3 :8 ie 8X = (9x - 400)

45.

An amount of money is distributed among A, B and C in the ratio of 1:2:9. If C gives Rs. 400 from his share to B, the new ratio becomes 1 : 3 : 8 . What is the total amount ?

Answer»

Rs. 4800

Let the amount received by A, B and C be x, 2X and 9X respectively.
∴ TOTAL = 12x
x : 2x + 400 : 9x - 400 = 1 : 3 :8
ie 8X = (9x - 400)

Discussion

46.	Find the mean proportional between 7921 & 9409?
Answer» 8633 Formula = √a×B A = 7921 and B = 9409 √7921×9409 = 89 × 97 = 8633

46.

Find the mean proportional between 7921 & 9409?

Answer»

8633

Formula = √a×B
A = 7921 and B = 9409
√7921×9409 = 89 × 97 = 8633

Discussion

47.	In a school the ratio of boys to girls is 3 : 5. When 12 girls leave the school, the ratio becomes 9 : 1 3 . How many boys are there in the school ?
Answer» 54 3x/5x - 12 = 9/13 = 108 = (45 - 39)X = x = 108/6 = 18 No. of boys = 3 x 18 = 54

47.

In a school the ratio of boys to girls is 3 : 5. When 12 girls leave the school, the ratio becomes 9 : 1 3 . How many boys are there in the school ?

Answer»

54

3x/5x - 12 = 9/13 = 108 = (45 - 39)X
= x = 108/6 = 18
No. of boys = 3 x 18 = 54

Discussion

48.	A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?
Answer» Rs.50 NA

48.

A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.350. How much does C have?

Answer»

Rs.50

NA

Discussion

49.	A number is equal to 40% of another number. What is the ratio of the first number to the second number ?
Answer» 7 : 10 Let the first NUMBER be X and the SECOND number be y. Then, 4/7 of x = 40% of y = 4/7 x x = 40/100 x y = 4/7 x = 2/5 y = x/y = 7/10 = 7 : 10

49.

A number is equal to 40% of another number. What is the ratio of the first number to the second number ?

Answer»

7 : 10

Let the first NUMBER be X and the SECOND number be y.
Then, 4/7 of x = 40% of y
= 4/7 x x = 40/100 x y
= 4/7 x = 2/5 y
= x/y = 7/10 = 7 : 10

Discussion

50.	The respectively ratio of the present ages of Raju and Ram is 7 : 8 The sum of the their ages is 60. What will be the ratio of their ages 8 years hence?
Answer» 9 : 10 Let the present AGES of Raju and Ram be 7X and 8X YEARS respectively. According to the QUESTION, 7x + 8x = 60 Therefore, 15x = 60;

50.

The respectively ratio of the present ages of Raju and Ram is 7 : 8 The sum of the their ages is 60. What will be the ratio of their ages 8 years hence?

Answer»

9 : 10

Let the present AGES of Raju and Ram be 7X and 8X YEARS respectively.
According to the QUESTION, 7x + 8x = 60
Therefore, 15x = 60;

Discussion

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