Question

Three years hence, the ages of Radha and Meena will be in the ratio 5 : 2. If the sum of their present ages is 62 years, their ages, 2 years ago, were:

Options

• 43 years and 19 years

• 41 years and 17 years

• 40 years and 16 years

• none of these

Answer 1

none of these

Explanation:

Let the present ages of Radha and Meena be a and b.

It is given, three years hence, the ages of Radha and Meena will be in the ratio 5 : 2.

⇒ `(a + 3)/(b + 3)` = 52

⇒ 2(a + 3) = 5(b + 3)

⇒ 2a + 6 = 5b + 15

⇒ 2a = 5b + 15 − 6

⇒ 2a = 5b + 9

⇒ a = `(5b + 9)/2`    ....(1)

The sum of their present ages = 62 years.

The sum of their present ages = 62 years.

⇒ a + b = 62

Substituting the value of a from equation (1), we get

⇒ `(5b+9)/2 + b = 62`

⇒ 5b + 9 + 2b = 124

⇒ 7b + 9 = 124

⇒ 7b = 124 − 9

⇒ 7b = 115

⇒ b = `115/7`

Substituting the value of b in equation (1),

⇒ a = `(5 xx 115/7 + 9)/2`

⇒ a = `(575 + 63)/14`

⇒ a = `638/14`

⇒ a = `319/7`

Radha's age 2 years ago = a − 2

= `319/7 - 2`

= `(319 - 14)/7`

= `305/7`

= 43.57

Meena's age 2 years ago = b − 2 

= `115/7 - 2`

= `(115 - 14)/7`

= `101/7`

= 14.42