Two years ago the ages of Radha and Meena were in the ratio 5 : 2. If the sum of their present ages is 39 years, their ages, 2 years ago, were :

1. 27 years and 12 years

2. 17 years and 22 years

3. 25 years and 10 years

4. 11 years and 28 years

Let present ages of Radha and Meena be x and y years respectively.

Given,

Sum of present ages = 39

⇒ x + y = 39

⇒ x = 39 - y ……..(1)

Given,

Two years ago the ages of Radha and Meena were in the ratio 5 : 2.

$\Rightarrow \dfrac{x - 2}{y - 2} = \dfrac{5}{2} \\[1em] \Rightarrow \dfrac{39 - y - 2}{y - 2} = \dfrac{5}{2} \\[1em] \Rightarrow \dfrac{37 - y}{y - 2} = \dfrac{5}{2} \\[1em] \Rightarrow 2(37 - y) = 5(y - 2) \\[1em] \Rightarrow 74 - 2y = 5y - 10 \\[1em] \Rightarrow 5y + 2y = 74 + 10 \\[1em] \Rightarrow 7y = 84 \\[1em] \Rightarrow y = \dfrac{84}{7} = 12.$

x = 39 - y = 39 - 12 = 27.

∴ Radha's age = 27 years and Meena's age = 12 years.

Two years ago their age were :

x - 2 = 27 - 2 = 25 years and y - 2 = 12 - 2 = 10 years.

Hence, Option 3 is the correct option.