There are large number of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:
- 1.To buy 78 gm of coins one must buy at least 7 coins.
- 2.To weigh 78 gm using these coins one can use less than 7 coins.
Which of the statements given above is/are correct?
Answer & explanation
Answer: (c) Both 1 and 2
Making 78 gm as a sum of these coins needs at least 7 coins, for example 50 + 10 + 10 + 2 + 2 + 2 + 2. But on a two-pan balance coins can go on both pans: 50 + 25 + 5 against the object plus a 2 gm coin weighs 78 gm with just 4 coins.
- Statement 1 (buying 78 gm of coins): the coin weights must add up to exactly 78.
- 50 + 25 = 75 leaves 3, which 2 and 5 cannot make. 50 + 10 + 10 = 70 leaves 8 = 2 + 2 + 2 + 2, giving 7 coins; checking all combinations, none with 6 or fewer coins makes 78.
- So at least 7 coins must be bought — correct.
- Statement 2 (weighing 78 gm): put 50 + 25 + 5 = 80 gm on one pan and the object with a 2 gm coin on the other; the object weighs 80 − 2 = 78 gm.
- That uses 4 coins, fewer than 7 — correct.
- ✓ 1. The fewest coins adding up to 78 gm is 7 (50 + 10 + 10 + 2 + 2 + 2 + 2).
- ✓ 2. Using both pans of a balance, 50 + 25 + 5 on one side and 2 with the object on the other weighs 78 gm with 4 coins.
Remember · Buying uses sums of coin values only; weighing on a balance allows coins on both pans, so differences count too.
Question and answer: UPSC's official GS Paper II (2023, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·