type 2 age based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on ratio & proportion topic of quantitative aptitude

Questions : The ratio between Sumit’s and Prakash’s age at present is 2 : 3. Sumit is 6 years younger than Prakash. The ratio of Sumit’s age to Prakash’s age after 6 years will be

(a) 4 : 3

(b) 3 : 4

(c) 1 : 2

(d) 2 : 3

The correct answers to the above question in:

Answer: (b)

Sumit’s present age

= 2x years

Prakash’s present age

= 3x years

3x - 2x = 6 ⇒ x = 6

Required ratio

= (2 × 6 + 6) : (3 × 6 + 6)

= 18 : 24 = 3 : 4

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Read more age based ratio and proportion problems Based Quantitative Aptitude Questions and Answers

Question : 1

The ratio of the ages of two persons is 4 : 7 and the age of one of them is greater than that of the other by 30 years. The sum of their ages (in years) is

a) 70

b) 40k

c) 100

d) 110

Answer: (d)

Ages of the persons

= 4x and 7x years.

7x - 4x = 30

3x = 30 ⇒ x = 10

Sum of their ages

= 4x + 7x = 11x years

= 11 × 10 = 110 years

Question : 2

The present ages of A and B are in the ratio 3 : 4. Ten years ago, this ratio was 4 : 7. The present ages of A and B are respectively :

a) 24 years, 32 years

b) 27 years, 36 years

c) 21 years, 28 years

d) 18 years, 27 years

Answer: (d)

A’s present age = 3x years (let)

B’s present age = 4x years

According to the question,

10 years ago,

${3x - 10}/{4x - 10} = 4/7$

21x - 70 = 16x - 40

21x - 16x = 70 - 40

5x = 30

$x = 30/5$ = 6

A’s present age

= 3x = 3x × 6 = 18 years

B’s present age

= 4x = 4 × 6 = 24 years

Question : 3

The ratio of the age of Ram and Rahim 10 years ago was 1 : 3. The ratio of their age five years hence will be 2 : 3. Then the ratio of their present age is

a) 3 : 4

b) 2 : 5

c) 3 : 5

d) 1 : 2

Answer: (c)

Let the age of Ram and Rahim 10 years ago be x and 3x years respectively.

After 5 years from now,

${x + 15}/{3x +15} = 2/3$

6x + 30 = 3x + 45

3x = 45 - 30 = 15

x = 5

Ratio of their present age

= (x + 10) : (3x + 10)

= 15 : 25 = 3 : 5

Question : 4

Eighteen years ago, the ratio of A’s age to B’s age was 8 : 13. Their present ratios are 5 : 7. What is the present age of A ?

a) 50 years

b) 40 years

c) 70 years

d) 60 years

Answer: (a)

18 years ago,

A’s age = 8x years

B’s age = 13x years

At present,

${8x + 18}/{13x + 18} =5/7$

56x + 126 = 65x + 90

65x - 56x = 126 - 90

9x = 36

$x = 36/9$ = 4

A’s present age

= 8x + 18

= 8 × 4 + 18 = 50 years

Question : 5

The ratio of the ages of A and B at present is 3:1. Four years earlier the ratio was 4:1. The present age of A is

a) 36 years

b) 32 years

c) 40 years

d) 48 years

Answer: (a)

A’s present age = 3x years

B’s present age = x years

4 years ago,

${3x - 4}/{x -4} = 4/1$

4x - 16 = 3x - 4

4x - 3x = 16 - 4

x = 12

A’s present age

= 3x = 3 × 12 = 36 years

Question : 6

The present age of two persons are 36 and 50 years respectively. If after n years the ratio of their age will be 3 : 4, then the value of n is

a) 6

b) 3

c) 7

d) 4

Answer: (a)

${36 + n}/{50 + n} = 3/4$

144 + 4n = 150 + 3n

4n - 3n = 150 - 144

n = 6

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