Question

If 10 employees in an organization having an average weight of 73 kg leave and 5 employees having an average weight of 70 kg join, the average weight of the employees in the organization decreases by 0.4 kg. The average weight of all employees in the organization initially is 70 kg. If the number of employees initially in the organization is n, which of the following is/are correct?

I. 73 employees are left

II. n is a multiple of 16

III. 70 < n < 80

1.

Only I

2.

Only II

3.

Only III

4.

I and III

Answer 1

Correct Answer - Option 2 :

Only II

Given:

Average weight of n employees = 70 kg

Average weight of 10 employees who leave = 73 kg

Average weight of 5 employees who join = 70 kg

Difference in average weight = 0.4 kg

Formula Used:

Average = Sum of values/Number of values

Calculation:

Sum of the weight of 10 employees who leave/10 = 73 kg

⇒ Sum of the weight of 10 employees who leave = 730 kg

Sum of the weight of 5 employees who join/5 = 70 kg

⇒ Sum of the weight of 5 employees who join = 350 kg

Sum of the weight of n employees/n = 70 kg

⇒ Sum of the weight of n employees = 70n kg

∵ 10 employees leave and 5 join

∴ Number of employees left = n – 5

Sum of the weight of n – 5 employees/(n – 5) = 70 – 0.4

⇒ Sum of the weight of n – 5 employees = 69.6(n – 5)

⇒ 70n – 730 + 350 = 69.6n – 348

⇒ 0.4n = 32

⇒ n = 80 kg

I. 73 employees are left

80 – 10 + 5 = 75

⇒ I is not correct

II. n is a multiple of 16

80 = 5 × 16

⇒ II is correct

III. 70 < n < 80

⇒ 70 < n = 80

⇒ III is not correct

∴ Only II is correct