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A, B, C and D are four friends, each of whom weighs less than 100 kg. From amongst them they form a group and find the total weight of that group. If the sum of the total weights of all possible distinct groups, each having the same number of members as in the first is 882 kg, then what is the average weight of the four friends?1 point41.75 kg63.5 kg73.5 kgnone of these

Question

A, B, C and D are four friends, each of whom weighs less than 100 kg. From amongst them they form a group and find the total weight of that group. If the sum of the total weights of all possible distinct groups, each having the same number of members as in the first is 882 kg, then what is the average weight of the four friends?1 point41.75 kg63.5 kg73.5 kgnone of these

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Solution

The problem can be solved by understanding the concept of combinations in mathematics.

Here are the steps to solve the problem:

  1. We have 4 friends: A, B, C, and D. They can form groups of 1, 2, 3, or 4 members.

  2. The total weight of all possible distinct groups is given as 882 kg.

  3. If we consider groups of 1 member, there are 4 such groups (A, B, C, D).

  4. If we consider groups of 2 members, there are 6 such groups (AB, AC, AD, BC, BD, CD).

  5. If we consider groups of 3 members, there are 4 such groups (ABC, ABD, ACD, BCD).

  6. If we consider groups of 4 members, there is 1 such group (ABCD).

  7. So, the total number of all possible groups is 4 (for 1 member) + 6 (for 2 members) + 4 (for 3 members) + 1 (for 4 members) = 15 groups.

  8. Given that the total weight of all these groups is 882 kg, the total weight of the 4 friends (which is the weight of the group ABCD) can be calculated as follows: (882 kg / 15 groups) = 58.8 kg.

  9. Since the total weight of the 4 friends is 58.8 kg, the average weight of the friends is (58.8 kg / 4 friends) = 14.7 kg.

So, the average weight of the four friends is 14.7 kg. Therefore, the answer is "none of these".

This problem has been solved

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