Question

18. The average age of 5 persons in a group is increased
by 10 years when two men aged 30 years and 40
years are substituted by two women. Find the aver-
age age (in years) of the two women.
(a) 60
(b) 65
(c) 51
(d) 62
mm​

Answer 1

Answer: What is the average age of these two women ?  a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women.

Step-by-step explanation:

Answer 2

Given:

The average age of 5 persons in a group is increased by 10 years when two men aged 30 years and 40 years are substituted by two women.

To find:

The average age (in years) of the two women.

Solution:

We know,

$\boxed{\bold{Average = \frac{Sum \:of\:observations}{No. \:of\:observations} }}$

Let "x" years represents the average age of 5 persons of the group.

Then,

The sum of ages of 5 persons = 5x

Also, let "a" years and "b" years represent the ages of the two women who replace the two men.

Now, as given in the question, the final equation will be,

$\frac{5x - 30 - 40 + (a + b)}{5} = x + 10$

$\implies 5x -70+ (a +b) = 5x + 50$

$\implies (a +b) = 50 + 70$

$\implies (a +b) = 120$

on dividing by 2 on both sides of the equation

$\implies \frac{a + b}{2} = \frac{120}{2}$

$\implies \frac{a + b}{2} = 60$

since a and b are the age of the two women so the average of their ages will be $\frac{a + b}{2}$

$\implies \bold{Average \:age \:of\: the \:2 \:women = 60\:years}$ ← option (a)

Thus, the average age (in years) of the two women is → 60 years.

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