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

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

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

Answer: (c)

Let the present age of A and B be 4x and 5x years respectively,

According to the question,

${4x + 5}/{5x + 5} = 5/6$

25x + 25 = 24x + 30

x = 30 - 25 = 5

A’s present age

= 4x = 4 × 5 = 20 years

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

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

Answer: (c)

Let father’s age be 5x years.

Son’s age = 2x years

5x × 2x = 1000

$x^2$ = 100 ⇒ x = 10

Father’s age after 10 years

= 5x + 10

= 5 × 10 + 10 = 60 years