Question

The average age of 10 men increases by 3 years when one of them, whose age is 54 years is replaced by a woman. What is the age of the woman?

Answer 1

(54+x)/10=n

x=10n-54

x+y/10 = n+3

(10n-54+y)/10=n+3

10n-54+y = 10n+30

y-54 = 30

y= 30+54

y=84(age of women)

Answer 2

Given :

The average age of 10 men increases by 3 years when one of them, whose age is 54 years is replaced by a woman.

To Find:

What is the age of the woman?

Solution:

Let the average age of 10 men be x

$Average = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Average = \frac{\text{Sum of ages of 10 men}}{10}\\x= \frac{\text{Sum of ages of 10 men}}{10}\\10x=\text{Sum of ages of 10 men}$

The average age of 10 men increases by 3 years when one of them, whose age is 54 years is replaced by a woman

Let age of women be y

New Average age = x+3

New Sum = 10x-54+y

So,$x+3=\frac{10x-54+y}{10}\\10x+30=10x-54+y$

84=y

Hence the age of the woman is 84 years.