type 2 age based ratio & proportion problems Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC CGL Tier-1 2011]

At present, the ratio of the age of Maya and Chhaya is 6 : 5 and fifteen years from now, the ratio will get changed to 9 : 8. Maya’s present age is

a) 30 years

b) 40 years

c) 24 years

d) 21 years

Answer: (a)

Let Maya’s present age be 6x years and Chhaya’s present age be 5x years.

After 15 years,

${6x + 15}/{5x + 15} = 9/8$

48x + 120 = 45x + 135

48x - 45x = 135 - 120

3x = 15 ⇒ x = 5

Maya’s present age = 6x

= 6 × 5 = 30 years

Question : 7 [SSC CGL Prelim 2003]

My grandfather was 9 times older than me 16 years ago. He will be 3 times of my age 8 years from now. Eight years ago, the ratio of my age to that of my grandfather was

a) 1 : 2

b) 1 : 5

c) 2 : 5

d) 3 : 8

Answer: (b)

16 years ago,

My age = x years

My grandfather’s age = 9x years

After 8 years from the present,

9x + 16 + 8 = 3(x + 8 + 16)

9x + 24 = 3x + 24 + 48

9x + 24 = 3x + 72

9x - 3x = 72 - 24

6x = 48

$x = 48/6$ = 8

Required ratio 8 years ago,

= (x + 8) : (9x + 8)

= (8 + 8) : (9 × 8 + 8)

= 16 : 80 = 1 : 5

Question : 8 [SSC CGL Tier-I 2016]

The ratio of A’s age to B’s age is 4 : 3. ‘A’ will be 26 years old after 6 years. The age of B now is :

a) 21 years

b) 15 years

c) 12 years

d) 19$1/2$ years

Answer: (b)

A’s present age

= 4x years (let).

According to the question,

4x + 6 = 26

4x = 26 - 6 = 20

$x = 20/4$ = 5

B’s present age

= 3x = 3 × 5 = 15 years

Question : 9 [SSC SO 2006]

The ratio of the ages of a father and his son 10 years hence will be 5 : 3, while 10 years ago, it was 3:1. The ratio of the age of the son to that of the father today, is

a) 2 : 3

b) 2 : 5

c) 1 : 3

d) 1 : 2

Answer: (d)

Let the age of father 10 years hence is 5x years,

then age of son 10 years hence will be 3x years.

According to the question,

${5x - 10 - 10}/{3x - 10 - 10} = 3/1$

${5x - 20}/{3x - 20} = 3/1$

5x - 20 = 9x - 60

4x = 40 or x = 10

Required ratio

= (3x - 10) : (5x - 10)

= 20 : 40 = 1 : 2

Question : 10 [SSC CGL Prelim 2007]

The sum of the age of a father and his son is 100 years now. 5 years ago their age were in the ratio of 2 : 1. The ratio of the age of father and son after 10 years will be

a) 10 : 7

b) 3 : 5

c) 4 : 3

d) 5 : 3

Answer: (d)

5 years ago, let the age of father = 2x years (let)

Then, Age of son = x years

2x + 5 + x + 5 = 100

3x = 100 - 10 = 90

$x = 90/3$ = 30

Father’s present age

= 2x + 5 = 60 + 5 = 65 years

Son’s present age = x + 5

= 30 + 5 = 35 years.

After 10 years,

Ratio = ${65 + 10}/{35 + 10}$

$75/45 = 5/3$ = 5 : 3

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