CAT 2026 Slot 1 DILR Q11: Maths-based / Combinations

The set

A cash counter distributes exactly ₹6,000 per transaction using ₹100, ₹200 and ₹500 notes. Each customer specifies one of these three denominations as their preferred denomination. The counter distributes notes such that the number of notes of the customer's preferred denomination exceeds the total number of notes of the other two denominations.

TITA (type the answer) · +3 / 0

What is the number of ₹500 notes required to serve 50 customers who prefer ₹500 notes and another 50 customers who prefer ₹100 notes, if the total number of notes distributed is to be the smallest possible?

Your answer

Answer and solution

Correct answer: 1050

Solution

In ₹100 units: $a + 2b + 5c = 60$.
Prefer ₹500: fewest notes $= 12$ notes of ₹500.
Prefer ₹100 ($a > b + c$): fewest notes $= 23$ with $a = 13, b = 1, c = 9$ ($1300 + 200 + 4500$; $13 > 10$). No 22-note option exists.
₹500 notes $= 50 \times 12 + 50 \times 9 = 600 + 450 = 1050$

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