CAT 2026 Slot 1 DILR: Set 3: Cash counter — ₹100, ₹200, ₹500 notes with Solutions

4 questions: Q11, Q12, Q13, Q14. Solve each one here: tap the answer, press Check, then open the solution.

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.

Question 11Maths-based / Combinations

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 $= 50 \times 12 + 50 \times 9 = 600 + 450 = 1050$

Question 12Maths-based / Combinations

TITA (type the answer) · +3 / 0

What is the maximum number of customers that the counter can serve with a stock of fifty ₹500 notes and a sufficient number of notes of other denominations, if all customers are to be served with at most 20 notes per transaction?

Your answer

Answer and solution

Correct answer: 7

Solution

Prefer ₹100 needs at least 23 notes — impossible within 20.
Prefer ₹200 within 20 notes: fewest ₹500 notes is 7 ($a = 1, b = 12, c = 7$; $12 > 8$).
Prefer ₹500 needs at least 9 ₹500 notes.
So 7 per customer: $\lfloor 50/7 \rfloor = 7$ customers.

Question 13Maths-based / Combinations

MCQ · +3 / −1

In how many different ways can the counter serve a customer who prefers ₹500 notes?

Answer and solution

Correct answer: C

Solution

$a + 2b + 5c = 60$ with $c > a + b$:
$c = 12$: (0,0) → 1
$c = 11$: (5,0), (3,1), (1,2) → 3
$c = 10$: (8,1), (6,2), (4,3), (2,4), (0,5) → 5 [(10,0) fails]
$c = 9$: (1,7) → 1
Total $= 10$

Question 14Maths-based / Combinations

TITA (type the answer) · +3 / 0

If the counter can serve only 10 customers with a stock of 60 ₹500 notes and a sufficient number of notes of other denominations, what is the maximum number of customers who can have ₹500 notes as their preference?

Your answer

Answer and solution

Correct answer: 6

Solution

Fewest ₹500 notes for a ₹500-preferring customer is 9 ($1 \times ₹100 + 7 \times ₹200 + 9 \times ₹500$; $9 > 8$). [Doc said 10 — corrected; answer unchanged.]
$\lfloor 60/9 \rfloor = 6$ customers. The other 4 can be served with no ₹500 notes (e.g. 30 × ₹200).

An expected paper by Cetking, not the actual CAT paper. CAT is conducted by the IIMs.