There are 5 bags labeled 1 to 5. All the coins in a given bag have the same…
2014
There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is ___.
Attempted by 45 students.
Show answer & explanation
Correct answer: 12
Key idea: treat 10 gm as the base weight and each 11 gm coin adds 1 gm extra.
Total coins taken = 1 + 2 + 4 + 8 + 16 = 31. If all coins were 10 gm, total weight = 31 × 10 = 310 gm.
Actual total weight is 323 gm, so the extra weight from 11 gm coins is 323 − 310 = 13 gm. Each 11 gm coin contributes 1 gm extra, so the sum of the counts of coins taken from bags that are 11 gm must be 13.
Find which taken counts add to 13 using the available counts 1, 2, 4, 8, 16. We have 13 = 8 + 4 + 1, so the bags that contributed 11 gm coins are the ones from which 8, 4, and 1 coins were taken — these are the bags labeled 4 (8 coins), 3 (4 coins), and 1 (1 coin).
Product of their labels = 4 × 3 × 1 = 12.
Answer: 12