Question

The average weight of $3$ members of a family is $78\text{kg}$. If the weight of fourth member is added, then the average weight of $4$ members becomes $72\text{kg}$. Find the weight of the fourth member.

• A. $75\text{kg}$
• B. $54\text{kg}$
• C. $37.5\text{kg}$
• D. $72\text{kg}$

Answer 1

The correct option is B $54\text{kg}$

The formula to calculate the mean or average is,

$\text{Mean}=\frac{\text{Sum of all data points}}{\text{Total number of data points}}$

Given, the average weight of $3$ members of a family is $78\text{kg}$. Let their sum of weights is denoted by $A$.
Substitute these values in the formula of mean, to calculate the sum of weight of $3$ members.

$\begin{array}{cc}\text{Average weight of}3\text{members}& =\frac{\text{Sum of their weights}}{3}\\ 78& =\frac{A}{3}\\ A& =78\times 3\\ A& =234\end{array}$

Thus, the sum of weights of $3$ members of a family is $234\text{kg}$.

Now, a fourth member is added, such that the average weight of $4$ members becomes $84\text{kg}$. Let the weight of fourth member be denoted by $B$.

To obtain the weight of the fourth member, substitute these values in the formula of mean as follows,

$\begin{array}{cc}\text{Average weight of}4\text{members}& =\frac{\text{Sum of their weights}}{4}\\ 72& =\frac{A+B}{4}\\ 72& =\frac{234+B}{4}\\ 234+B& =72\times 4\\ 234+B& =288\\ B& =288-234\\ B& =54\end{array}$

Hence, the weight of the fourth member is $54\text{kg}$.