Question

The average weight of 10 men is decreased by 3 kg when one of them whose weight is 80 kg is replaced by a new person. The weight of the new person is
(A) 70
(B) 80
(C) 50
(D) 73

Answer 1

Hint: We are given the average weight of ten men and that they decrease by 3 kg when a person weighing 80 kg is replaced by another new person. We are asked in the question to find the weight of the new person with the given information. We will first let the sum of the nine men be ‘a’ kg and let the weight of the new person be ‘b’ kg. Average refers to the ratio of the sum of the given terms and the number of terms. Based on the given statement, we have the expression as, \[\dfrac{a+80}{10}-3=\dfrac{a+b}{10}\]. We will solve the expression and find the value of the weight of the new person. Hence, we will have the required weight.

Complete step by step answer:
According to the given question, we are given the average weight of ten men and that they decrease by 3 kg when a person weighing 80 kg is replaced by another new person. We have to find the weight of the new person.
Let the weight of the nine men be ‘a’ kg
And the weight of the new person be ‘b’ kg
As per the statement given to us in the question, we have the expression as,
\[\dfrac{a+80}{10}-3=\dfrac{a+b}{10}\]
We will now solve for ‘b’. taking the LCM in the LHS, we get,
\[\Rightarrow \dfrac{a+80}{10}-3\times \dfrac{10}{10}=\dfrac{a+b}{10}\]
\[\Rightarrow \dfrac{a+80}{10}-\dfrac{30}{10}=\dfrac{a+b}{10}\]
Taking the terms together, we get,
\[\Rightarrow \dfrac{a+80-30}{10}=\dfrac{a+b}{10}\]
\[\Rightarrow a+80-30=a+b\]
Cancelling ‘a’ from both the sides and calculating the value of ‘b’, we have,
\[\Rightarrow a+50=a+b\]
\[\Rightarrow b=50kg\]

So, the correct answer is “Option C”.

Note: The expression should be correctly formed as per the given information. The 3kg is decreased in the original weight of the ten men when the new person wasn’t accommodated and so do not write it otherwise the entire solution will get wrong. Also, the calculation should be done step wise and correctly.