There are 5 bags labelled 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 ________

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A is the number of coins of 10 gm and B is the number of coins of 11 gm.

A x 10 + B x 11 = 323

A + B = 31(Sum of all coins) multiply this equation with 10 and subtract from above equation we get

B = 13 and A = 18

B = 13 (only one combination: 8 4 1)

8 coins picked from bag labelled by 4.

4 coins picked from bag labelled by 3.

1 coin picked from bag labelled by 1.

Multiplication of all labels = 4 × 3 × 1 = 12

Hence 12 is the correct answer.

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