Question

The average age of a group of people is increased by 10 when a person aged 19 years is replaced by a new person aged 59 years. How many people are there in the group?

Answer 1

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Answer 2

Given,

The average age of a group of people increases by 10 years when a person of age 19 years is replaced by a person of age 59 years

To Find,

The number of persons in the group.

Solution,

Let us say the number of persons in the group = $x$

Let us say the sum of ages of the persons in the group = $a$

Let us say the average age of the persons in the group = $y$

Thus from the given statements, it can be deduced that $\frac{a}{x} = y$

⇒ $a = xy$

Now a person of age 19 years is removed and a person of age 59 years is added

⇒ $\frac{a-19+59}{x} = y +10$

⇒ $a + 40 = xy + 10x$

⇒ $xy + 40 = xy + 10x$ (since $a = xy$)

⇒ $40 = 10x$

⇒ $x = 4$

Henceforth, the number of persons in the group is 4.