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

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

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

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

Answer: (a)

Sonali’s present age

= 5x years

Monali’s present age = 3x years

According to the question,

After 5 years,

${5x + 5}/{3x + 5} =10/7$

${x +1}/{3x + 5} = 2/7$

7x + 7 = 6x + 10

7x - 6x = 10 - 7

x = 3

Monali’s present age

= 3x = 9 years

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: (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