Multiple choice

There are some chocolates and packets of biscuits kept in a big box. The average weight of the packets of biscuits in the box is 88 grams, and the average weight of the chocolates in the box is 60 grams. The average weight of both a chocolate and a packet of biscuits is 81 grams. Quantity A Number of packets of biscuits in the box Quantity B Number of chocolates in the box

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
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A Correct answer
Explanation

Using the alligation method: Biscuits (88) and Chocolates (60) average to 81. The ratio of biscuits to chocolates is (81-60) : (88-81) = 21 : 7 = 3 : 1. Since the ratio of biscuits to chocolates is 3:1, there are more biscuits than chocolates.

AI explanation

Using the method of alligation, the ratio of the number of biscuit packets to the number of chocolates is inversely proportional to their distances from the combined average. The difference between the biscuit average and the combined average is 88 minus 81, which is 7 grams. The difference between the chocolate average and the combined average is 81 minus 60, which is 21 grams. The ratio of biscuits to chocolates is therefore 21 to 7, or 3 to 1, meaning there are more packets of biscuits, so Quantity A is greater.

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