CAT 2022 Slot 1 · Quant · Question 20

Let there be n original students averaging w kg, and m new students.

The new students average w+3 kg.

After they join, the combined average is w+0.6, since 600 gm is 0.6 kg.

The total weight is nw+m\left( w+3 \right), spread over n+m students.

So \frac{nw+m\left( w+3 \right)}{n+m}=w+0.6.

Multiplying out, nw+mw+3m=\left( n+m \right)w+0.6\left( n+m \right).

The w terms cancel from both sides, leaving 3m=0.6\left( n+m \right).

Expanding, 3m=0.6n+0.6m, so 2.4m=0.6n.

Dividing, \frac{n}{m}=\frac{2.4}{0.6}=4.

So the ratio of original to new students is 4:1 — the fourth option.

Shortcut. Think in terms of the shift: each new student arrives 3 kg above the old average, and that surplus must lift all n+m students by 0.6 kg. So 3m=0.6\left( n+m \right), which rearranges to n=4m in one line — the average weight w never matters.