There are large numbers of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements: To buy 78 gm of coins one must buy at least 7 coins. To weigh 78 gm using these coins one can use less than 7 coins. Which of the statements given above is/are correct?

Q 98 / 370

UPSC CSE Prelims 2023

There are large numbers of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:

To buy 78 gm of coins one must buy at least 7 coins.
To weigh 78 gm using these coins one can use less than 7 coins.

Which of the statements given above is/are correct?

EXPLANATION

Correct Option (1)

Statement 1 asserts that to acquire 78 gm of coins, a minimum of 7 coins must be purchased. To achieve a total weight of 78 gm using the available denominations (2 gm, 5 gm, 10 gm, 25 gm, 50 gm), one combination that minimizes the number of coins is as follows:

One 50 gm coin
Two 10 gm coins (2 × 10 = 20 gm)
Four 2 gm coins (4 × 2 = 8 gm)

The total weight for this combination is 50 gm + 20 gm + 8 gm = 78 gm. The total number of coins used is 1 + 2 + 4 = 7 coins. This combination represents the minimum number of coins required to sum to 78 gm using the given denominations. Therefore, statement 1 is correct.

Incorrect Options:

Statement 2 claims that 78 gm can be weighed using less than 7 coins. As established in the explanation for Statement 1, the minimum number of coins required to achieve a total weight of 78 gm is 7. Since 7 is the minimum count, it is not possible to use fewer than 7 coins to reach this exact weight. Consequently, statement 2 is incorrect.