Question

Three years ago, The average of A and B is 18years with join of C the average becomes 22 years. How old is 'C' now.​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The present age of C is 33

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Average of A and B = 18 years

When C joins, Average = 22 years

To Find :

Present age of C

Solution :

$\textbf{\underline{\underline{Case I}}}$

Here,

Average (Mean) = 18

Observations = 2

Sum of Observations = x

★ $\boxed{\sf{Mean = \frac{Sum \: of \: Observations}{No. \: of \: Observations}}}$

$\sf{\implies} \: 18 = \dfrac{x}{2}$

$\sf{\implies} \: 18 \times 2 = x$

$\sf{\implies} \: x = 36$

Sum of Observations is 36

$\rule{300}{1.5}$

$\textbf{\underline{\underline{Case II}}}$

Consider the age of C as y

Here,

Observations = 3

Mean = 22

Sum of Observations = 36 + y (as age of C is added)

$\sf{\implies} \: 22 = \dfrac{36 + y}{3}$

$\sf{\implies} \: 22 \times 3 = 36 + y$

$\sf{\implies} \: 66 = 36 + y$

$\sf{\implies} \: y = 66 - 36$

$\sf{\implies} \: y = 30$

The age of C is 30 (3 Years ago)

$\rule{300}{1.5}$

But it is mentioned in the question that the average is before 3 years. The present age of C =

$\sf{\implies} \: 30 + 3$

$\sf{\implies} \: 33$

$\therefore$ The present age of C is 33