मान लीजिए, आपके पास तीन मूल्य-वर्गों, ₹ 1, ₹ 10 और ₹ 50, में रुपया मुद्रा पर्याप्त मात्रा में है । आप ₹ 107 के एक बिल का भुगतान कितने विभिन्न तरीकों से कर सकते हैं ?
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Suppose you have sufficient amount of rupee currency in three denominations: ₹ 1, ₹ 10 and ₹ 50. In how many different ways can you pay a bill of ₹ 107?
(a) 16 · (b) 17 · (c) 18 · (d) 19
उत्तर और व्याख्या · explanation in English
Answer: (c) 18
Count by the number of ₹50 notes. With none, ₹107 can include 0 to 10 ten-rupee notes (11 ways); with one, ₹57 can include 0 to 5 (6 ways); with two, ₹7 uses only ₹1 coins (1 way). Total 18.
- No ₹50 note: ₹107 = 10a + b with a = 0, 1, …, 10 → 11 ways.
- One ₹50 note: ₹57 = 10a + b with a = 0, 1, …, 5 → 6 ways.
- Two ₹50 notes: ₹7 = 10a + b needs a = 0 → 1 way.
- In each case ₹1 coins make up the balance, so each choice is one way.
- Total = 11 + 6 + 1 = 18.
Remember · For currency combinations, fix the largest denomination, count choices for the next; the smallest always fills the rest.
Question and answer: UPSC's official GS Paper II (2019, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·