A bill for ₹1,840 is paid in the denominations of ₹50, ₹20 and ₹10 notes. 50 notes in all are used. Consider the following statements:
- 1.25 notes of ₹50 are used and the remaining are in the denominations of ₹20 and ₹10.
- 2.35 notes of ₹20 are used and the remaining are in the denominations of ₹50 and ₹10.
- 3.20 notes of ₹10 are used and the remaining are in the denominations of ₹50 and ₹20.
Which of the above statements are not correct?
Answer & explanation
Answer: (d) 1, 2 and 3
Let a, b, c be the numbers of ₹50, ₹20 and ₹10 notes. The two totals reduce to 4a + b = 134, and none of the three statements gives whole, non-negative numbers of notes, so all three are incorrect.
- Let the numbers of ₹50, ₹20 and ₹10 notes be a, b and c. Then a + b + c = 50 and 50a + 20b + 10c = 1840, that is 5a + 2b + c = 184.
- Subtract the first equation from the second: 4a + b = 134.
- Statement 1: a = 25 gives b = 134 − 100 = 34, and then c = 50 − 25 − 34 = −9. Impossible.
- Statement 2: b = 35 gives 4a = 99, which is not a whole number. Impossible.
- Statement 3: c = 20 gives a + b = 30; with 4a + b = 134 this means 3a = 104, not a whole number. Impossible.
- Check: a valid payment does exist, e.g. a = 30, b = 14, c = 6 — that is 50 notes and 1500 + 280 + 60 = ₹1,840 — so the bill itself is fine; only the three statements fail.
- ✗ 1. a = 25 forces c = −9, a negative number of ₹10 notes.
- ✗ 2. b = 35 forces 4a = 99, so a is not a whole number.
- ✗ 3. c = 20 forces 3a = 104, so a is not a whole number.
Remember · With a count total and a value total, subtract to get one clean equation, then test each statement for whole, non-negative answers.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·