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 age of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be

(a) $17/18$

(b) $11/12$

(c) $15/16$

(d) $22/24$

The correct answers to the above question in:

Answer: (a)

The present age of boys are 5x and 6x years respectively.

After 2 years,

${5x + 2}/{6x + 2} = 7/8$

42x + 14 = 40x + 16

2x = 2 ⇒ x = 1

Ratio after 12 years

5x + 12 : 6x + 12 = 17 : 18

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

Question : 1

The ratio of the present age of Puneet and Appu is 2 : 3. After 3 years the ratio of their age will be 3 : 4. The present age of Puneet is :

a) 9 years

b) 4 years

c) 6 years

d) 3 years

Answer: (c)

Let the present age of Puneet and Appu be 2x and 3x years respectively.

After 3 years,

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

9x + 9 = 8x + 12

x = 3

Present age of Puneet

= 2x = 2 × 3 = 6 years

Question : 2

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

Question : 3

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 : 4

The ratio of ages of two persons is 5 : 9 and the age of one of them is greater than the other by 40 years. The sum of their ages in year is

a) 150

b) 160

c) 140

d) 180

Answer: (c)

Age of first person = 5x years

Age of second person

= 9x years

According to the question,

9x - 5x = 40

4x = 40 ⇒ x = 10

Sum of their ages

= 5x + 9x = 14x

= 14 × 10 = 140 years

Question : 5

The present ages of A and B are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6 : 7. Then the present age of A in years is :

a) 33 years

b) 30 years

c) 32 years

d) 35 years

Answer: (d)

A’s present age = 5x years

B’s present age = 6x years

According to the question,

After 7 years,

${5x + 7}/{6x + 7} = 6/7$

36x + 42 = 35x + 49

36x - 35x = 49 - 42

x = 7

A’s present age

= 5x = 35 years

Question : 6

Four years ago, the ratio of A’s age to B’s age was 11 : 14 and four years later their age will be in the ratio 13 : 16. The present age of A is

a) 44 years

b) 28 years

c) 26 years

d) 48 years

Answer: (d)

Let the age of A and B four years ago be 11x and 14x years respectively.

According to the question,

After 4 years from now,

${11x + 8}/{14x + 8} = 13/16$

176x + 128 = 182x + 104

182x - 176x = 128 - 104

6x = 24 ⇒ $x = 24/6$ = 4

A’s present age = (11x + 4) years

= 11 × 4 + 4 = 48 years

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