Ratio of Ages Over Time

Let present ages of Rajesh and Garima be $R$ and $G$ respectively.

When Rajesh's age was $G$ (which was $R - G$ years ago):

• Rajesh's age $= G$
• Garima's age $= G - (R - G) = 2G - R$

Ratio was $3 : 2$: $\frac{G}{2G - R} = \frac{3}{2} \implies 2G = 6G - 3R \implies 3R = 4G \implies R = \frac{4}{3}G$

When Garima's age becomes $R$ (in $R - G$ years):

• Garima's age $= R$
• Rajesh's age $= R + (R - G) = 2R - G$

Ratio of Rajesh's age to Garima's age: $\frac{2R - G}{R} = 2 - \frac{G}{R} = 2 - \frac{3}{4} = \frac{5}{4}$

Thus, the ratio will become 5 : 4.