Question

The average age of 21 boys is 29 years. When one boy leaves the average age increased by 1/4 year. How old is the boy who leaves?

Answer 1

Answer:

The age of the boy who leaves is 24 years.

Step-by-step explanation:

The average age of 21 boys = 29 years

one boy leaves so,

the average age of 20 boys = (29 + 1/4) years

                                                      = (117/4) years

                                                      = 29.25 years

The total addition of ages of 21 boys = Average age of boys X the number of boys

                                                                          = (21 X 29) years

                                                                          = 609 years

The total addition of ages of 20 boys = (20 X 29.25) years

                                                                          = 585 years.

The age of the boy who leaves = total age of 21 boys - the total age of 20 boys

                                                        = (609 - 585) years

                                                        = 24 years.

Answer 2

The age of the boy who leaves is 24 years.

Solution :

Given, The average age of 21 boys is 29 years.

As We know that,

$\sf \: Average \: age = \dfrac{ Sum \: of \: ages}{ Number \: of \: people }$

From this, We can infer that, Sum of ages of all boys = 21 * 29 = 609 years.

Let the age of the boy who leaves out is m years.

Now,

The sum of remaining boys = 609 - m.

Number of boys remaining = 21 - 1 = 20

Average age of the remaining boys is now,

$= \dfrac{609 - m}{20}$

According to the question

The average age increases by 1/4. So the average age will be (29 + 1/4) years

$29 + \frac{1}{4} = \frac{609 - m}{20} \\ \\ \frac{117}{4} = \frac{609 - m}{20} \\ \\ \frac{117}{4} \times 20 = 609 - m \\ \\ 117 \times 5 = 609 - m \\ \\ 585 = 609 - m \\ \\ m = 609 - 585 = 24 \\ \\ \boxed{ \boxed{ \huge \: m = 24 \: years \: }}$

Therefore, The age of the boy who left is 24 years.