CAT 2023 Slot 2 · Quant · Question 16

If each of n people receives ₹352, the total amount is 352n.

In the second arrangement, two people take ₹506 each, using up 2\times 506=1012.

What remains is 352n-1012, shared equally among the other n-2 people.

Each of them receives \frac{352n-1012}{n-2}, and this is at most ₹330.

So \frac{352n-1012}{n-2}\le 330.

Since n>2, the denominator is positive and the inequality can be cross-multiplied safely: 352n-1012\le 330\left( n-2 \right).

Expanding the right side, 352n-1012\le 330n-660.

Collecting terms, 22n\le 352.

So n\le 16, and the maximum possible value is n=16.

Checking at n=16: the total is 352\times 16=5632, and after the two large shares 5632-1012=4620 is split among 14 people, giving exactly ₹330 each — which satisfies the condition.

Shortcut. Each of the two favoured people gains 506-352=154 over the equal share, a total gain of 308 taken from the other n-2 people. Each of those loses at least 352-330=22, so 22\left( n-2 \right)\le 308, giving n-2\le 14 and n\le 16 in one line.