CAT 2024 Slot 1 · Quant · Question 13

Work backwards from the end, where nothing is left.

Let the shop hold t kg just before the third customer. That customer takes \frac{t}{2}+3 and clears the stock, so \frac{t}{2}+3=t.

That gives \frac{t}{2}=3 and t=6 kg before the third sale.

Let the shop hold u kg before the second customer. After that sale, u-\left( \frac{u}{2}+3 \right)=\frac{u}{2}-3 remains, and this equals 6.

So \frac{u}{2}=9 and u=18 kg before the second sale.

Let the initial quantity be v kg. After the first sale, \frac{v}{2}-3 remains, and this equals 18.

So \frac{v}{2}=21 and v=42 kg.

Shortcut. Each step backwards is the same move: add 3, then double. Starting from 0 this gives 6, then 18, then 42 — three mental steps with no algebra at all.