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:

1. 43 years and 19 years

2. 41 years and 17 years

3. 40 years and 16 years

4. none of these

none of these

Reason

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.

$\Rightarrow \dfrac{a + 3}{b + 3} = \dfrac{5}{2}\\[1em] \Rightarrow 2(a + 3) = 5(b + 3)\\[1em] \Rightarrow 2a + 6 = 5b + 15\\[1em] \Rightarrow 2a = 5b + 15 - 6\\[1em] \Rightarrow 2a = 5b + 9\\[1em] \Rightarrow a = \dfrac{5b + 9}{2} \space ………. \space (1)$

The sum of their present ages = 62 years.

⇒ a + b = 62

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

⇒ $\dfrac{5b + 9}{2}$ + b = 62

⇒ 5b + 9 + 2b = 124

⇒ 7b + 9 = 124

⇒ 7b = 124 - 9

⇒ 7b = 115

⇒ b = $\dfrac{115}{7}$

Substituting the value of b in equation (1),

$\Rightarrow a = \dfrac{5 \times \dfrac{115}{7} + 9}{2}\\[1em] \Rightarrow a = \dfrac{575 + 63}{14}\\[1em] \Rightarrow a = \dfrac{638}{14}\\[1em] \Rightarrow a = \dfrac{319}{7}\\[1em]$

Radha's age 2 years ago = a - 2 = $\dfrac{319}{7} - 2 = \dfrac{319 - 14}{7} = \dfrac{305}{7} = 43.57$

Meena's age 2 years ago = b - 2 = $\dfrac{115}{7} - 2 = \dfrac{115 - 14}{7} = \dfrac{101}{7} = 14.42$

Hence, option 4 is the correct option.