Answer:
Total Weight of all the five boys is <em>234 kg</em>.
Step-by-step explanation:
Given that there are <em>five </em>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](https://tex.z-dn.net/?f=_5C_2%20%3D10)
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 = } \dfrac{88+90+91+92+93+94+95+96+98+99}{4}\\\Rightarrow \text{Total weight of boys = } \dfrac{936}{4}\\\Rightarrow \text{Total weight of boys = } 234\ kg](https://tex.z-dn.net/?f=%5Ctext%7BTotal%20weight%20of%20boys%20%3D%20%7D%20%5Cdfrac%7B88%2B90%2B91%2B92%2B93%2B94%2B95%2B96%2B98%2B99%7D%7B4%7D%5C%5C%5CRightarrow%20%5Ctext%7BTotal%20weight%20of%20boys%20%3D%20%7D%20%5Cdfrac%7B936%7D%7B4%7D%5C%5C%5CRightarrow%20%5Ctext%7BTotal%20weight%20of%20boys%20%3D%20%7D%20234%5C%20kg)
So, Total Weight of all the five boys is <em>234 kg</em>.