Question

Five boys weighed themselves in pairs in all possible combinations. The measured weights were 88 kg, 90 kg, 91 kg, 92 kg, 93 kg, 94 kg, 95 kg, 96 kg, 98 kg and 99 kg. The total weight of the five boys is:

Answer 1

Total Weight of all the five boys is 234 kg.

Explanation:

Given that there are five boys.

They have weighed themselves in pairs in all possible combinations.

And their weights are: 88 kg, 90 kg, 91 kg, 92 kg, 93 kg, 94 kg, 95 kg, 96 kg, 98 kg and 99 kg

To find: Total weights of the five boys = ?

Solution:

First of all, we need to find the total number of pairs that can be formed from a total of 5 number of boys.

Total number of pairs possible =
`_5C_2 =10`

If we select one boy, there are 4 other boys with whom pairs can be formed.

So, every boy's weight is repeated 4 number of times in these 10 pairs.

If we add all the 10 measured weights given and then divide them with 4 we will get the total weight of the five boys.

`\text{Total weight of boys = } (88+90+91+92+93+94+95+96+98+99)/(4)\\\Rightarrow \text{Total weight of boys = } (936)/(4)\\\Rightarrow \text{Total weight of boys = } 234\ kg`

So, Total Weight of all the five boys is 234 kg.