Question

the average age of a man and three boys is 15years,if the ages of the boys are 5, 8 and 15years, how old is the man?

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

The age of the man is 32 years.

$\textbf{\underline{\underline{Explanation :-}}}$

⛤ $\textsf{\underline{\underline{Given :}}}$

The average of their ages = 15 years.

Ages of the boys = 5, 8 and 15years

⛤ $\textsf{\underline{\underline{To find :}}}$

The age of the man

⛤ $\textsf{\underline{\underline{Solution :}}}$

Consider the age of the man as x

$\star$ As We know :

$\boxed{\sf{Mean = \frac{Sum \: of \: Observations}{Number \: of \: Observations}}}$

$\tt{\implies} \: 15 = \dfrac{5 + 8 + 15 + x}{4}$

$\tt{\implies} \: 15 = \dfrac{28 + x}{4}$

$\tt{\implies} \: 15 \times 4 = 28 + x$

$\tt{\implies} \: 60 = 28 + x$

$\tt{\implies} \: 32 = x$

$\tt{\implies}\red{\: x = 32}$

$\therefore$ The age of the man is 32 years.

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies} \: \dfrac{15 + 5 + 8 + 32}{4}$

$\tt{\implies} \: \dfrac{60}{4}$

$\tt{\implies} \: 15$

$\therefore$ The age of the man is 32 years.

Answer 2

Answer :-

32 years.

Step-by-step Explanation :-

Given :-

Average age of a man and three boys = 15 years ;

Ages of three boys = 5, 8 and 15 years.

To Find :-

Age of the man.

Let the age of man be x.

Solution :-

Average = $\dfrac{5 + 8 + 15 + x}{4}$

$\implies$15 = $\dfrac{28 + x}{4}$

$\implies$15 × 4 = 28 + x

$\implies$60 = 28 + x

$\implies$60 - 28 = x

$\implies$32 = x

So, the age of man is 32 years.

Verification :-

$\implies$15 = $\dfrac{5 + 8 + 15 + 32}{4}$

$\implies$15 = $\dfrac{60}{4}$

$\implies$15 = 15

Hence, Verified..!

So, The Age of man is 32 years.