Question

A factory has 130 workers. They were given certain scores based on their work. The average age of women is 14. The average age of men is 18. The average age of top 20 scorers is 17. What is the average age of the last 110 scorers if there are 70 men in the factory?
1. 17
2. 18
3. 15
4. 16

Answer 1

Correct Answer - Option 4 : 16

Given: A factory has 130 workers. They were given certain scores based on their work. The average age of women is 14. The average age of men is 18. The average age of top 20 scorers is 17.

Formula: Average of n numbers a1, a2, .… an = (a1 + a2 + ... + an)/n

Calculation:

There are 70 men in the factory then

No. of women = 130 – 70 = 60

Average age of 60 women = 14

Average age of 70 men = 18

Average age of total workers in factory = [14 × 60 + 18 × 70]/130

⇒ (840 + 1260)/130

⇒ (2100/130) = 210/13

Let the average age of the last 110 scorers be x.

Average age of top 20 scorers = 17

So, the average age of 130 scorers is

210/13 = (20 × 17 + 110 × x)/130

⇒ 2100 = 340 + 110x

⇒ 110x = 1760

⇒ x = 176/11 = 16

Hence, the average age of the last 110 scorers is 16.