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 of the present age of Rahul and Rashmi is 2 : 1. The ratio of their age after 30 years will be 7 : 6. What is the present age of Rahul ?

(a) 12 years

(b) 20 years

(c) 10 years

(d) 6 years

The correct answers to the above question in:

Answer: (a)

Let the present age of Rahul and Rashmi be 2x and x years respectively.

After 30 years,

${2x + 30}/{x +30} = 7/6$

12 x +180 = 7x + 210

12 x - 7x = 210 - 180

5 x = 30 ⇒ $x = 30/5 = 6$

Rahul’s present age

= 2x = 2×6 = 12 years

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

Question : 1

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

Question : 2

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 : 3

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 : 4

Four years ago, the ratio of the age of A and B was 2 : 3 and after four years it will become 5 : 7. Find their present age.

a) 40 years and 56 years

b) 36 years and 52 years

c) 32 years and 48 years

d) 36 years and 40 years

Answer: (b)

Four years ago let the age of A and B be 2x and 3x years respectively.

According to the question

${2x + 4 + 4}/{3x + 4 + 4} = 5/7$

${2x + 8}/{3x + 8} = 5/7$

14x + 56 = 15x + 40

x = 16

Present age of A

= 2x + 4 = 2 × 16 + 4 = 36 years

Present age of B

= 3x + 4

= 3 × 16 + 4 = 52 years

Question : 5

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

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

Question : 6

If 4 years ago the ratio between the ages of P and Q was 5 : 6 and the sum of their ages at present is 52 years, what is the ratio of their present ages ?

a) 7 : 8

b) 4 : 5

c) 6 : 7

d) 5 : 6

Answer: (c)

4 years ago,

P’s age = 5x years

Q’s age = 6x years

According to the question,

5x + 4 + 6x + 4 = 52

11x = 52 - 8 = 44

$x = 44/11$ = 4

Required ratio

= (5x + 4) : (6x + 4)

= (5 × 4 + 4) : (6 × 4 + 4)

= 24 : 28 = 6 : 7

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