The ratio of the ages of Ram and Rahim 10 years ago was 1 : 3. The ratio of their ages five years hence will be 2 : 3. Then the ratio of their present ages is

Let present ages of Ram and Rahim be $$x$$ and $$y$$ years respectively.

According to ques, ratio of their ages 10 years ago is :

=> $$\frac{x-10}{y-10}=\frac{1}{3}$$

=> $$3x-30=y-10$$

=> $$3x-y=20$$ ------------(i)

Also, five years hence, => $$\frac{x+5}{y+5}=\frac{2}{3}$$

=> $$3x+15=2y+10$$

=> $$2y-3x=5$$ -----------(ii)

Adding equation (i) and (ii),

=> $$y=20+5=25$$

Substituting it in equation (i), we get :

=> $$3x=20+25=45$$

=> $$x=\frac{45}{3}=15$$

$$\therefore$$ Ratio of Ram and Rahim's ages = $$\frac{15}{25}=\frac{3}{5}$$

=> Ans - (B)