CAT 2024 Slot 2 · Quant · Question 22

Let the present ages be R for Rajesh and G for Garima, with R>G.

Rajesh's age was G exactly R-G years ago.

At that time Garima's age was G-\left( R-G \right)=2G-R.

The ratio then was Rajesh to Garima, that is G:\left( 2G-R \right)=3:2.

Cross-multiplying, 2G=3\left( 2G-R \right), so 2G=6G-3R.

That gives 3R=4G, so R=\frac{4G}{3}.

Garima's age becomes R after R-G years.

At that future moment Rajesh's age will be R+\left( R-G \right)=2R-G.

Substituting R=\frac{4G}{3}, Rajesh will be \frac{8G}{3}-G=\frac{5G}{3} and Garima will be \frac{4G}{3}.

The ratio is \frac{5G}{3}:\frac{4G}{3}=5:4, the fourth option.

Shortcut. The age gap R-G never changes, and the three moments are spaced one gap apart. With 3R=4G, take G=3 and R=4, so the gap is 1: the ages run 3,2 then 4,3 then 5,4 — an arithmetic chain that gives 5:4 at a glance.