Question

The mean age of 5 children of a family is 12 years. If four of them are respectively 6,
11, 12 and 16 years of age, find the age of the fifth child.​

Answer 1

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The mean age of 5 children of a family is given i.e. 12 years and the ages of four children is also given. We will use this information from the question to get our answer. We will take the age of the fifth child as x and then will we find the mean. As we will solve it step-by-step, we will find our answer.

Answer :-

The age of the fifth child is 15 years.

Given :-

Mean age of 5 children of a family = 12 years

Total no. of children = 5

The ages of four children are 6, 11, 12, 16.

Formula used :-

$Mean\:\:age = \frac{Sum\:\:of\:\:all\:\:ages\:\:of\:\:the\:\:children}{Total\:\:no.\:\:of\:\:children}$

Solution :-

Let the age of 5th child be x.

Now the ages of five children are 6, 11, 12, 16, x.

$Mean\:\:age = \frac{Sum\:\:of\:\:all\:\:ages\:\:of\:\:the\:\:children}{Total\:\:no.\:\:of\:\:children}\\ \\=>12 =\frac{6+11+12+16+x}{5} \\ \\=> 12 \times5=45+x \\ \\=> 60 = 45+x\\ \\=> 60-45=x \\ \\ =>15 =x$

The age of the fifth child = x = 15 years.