Question

In a group of 24 people, the age of one person is twice that of another from the group. If these two are replaced by two people whose ages are 7 years and 5 years, the average age of the group decreases by 1 year. Find the age of the older of the two.
1. 22 years
2. 32 years
3. 26 years
4. 24 years
5. 35 years

Answer 1

Correct Answer - Option 4 : 24 years

Formula used:

Average = sum of observations/total number of observations

Calculation:

Let the average age of the class be x years and the ages of the replaced students are y and 2y.

Total age of class = 24x

Total age of the class excluding the replaced = 24x - 3y

A.T.Q

24x - 3y + 7 + 5 = 24(x - 1)

⇒ 24x - 3y + 12 = 24x - 24

⇒ 3y = 36

⇒ y = 12 years

so, 2y = 24 years

∴ The age is 24 years