Arithmatic Mean Question Answers

Weighted Average - CAT 2007 Math Preparation

Question 4 the day : November 10, 2006
The question for the day is a sample practice problem in Aritbmetic Mean, weighted Average, an Arithmetic Topic and the problem provides an understanding of simple and weighted average.

Question
The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the manager whose salary was Rs. 720, was replaced with a new manager, then the average salary of the team went down to 580. What is the salary of the new manager?

1. 570
2. 420
3. 690
4. 640

Correct Answer - 420. Choice (2)

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Explanatory Answer

The total salary amount = 15 * 600 = 9000
The salary of the exiting manager = 720.
Therefore, the salary of 12 workers and the remaining 2 managers = 9000 - 720 = 8280

When a new manager joins, the new average salary drops to Rs.580 for the total team of 15 of them.
The total salary for the 15 people i.e., 12 workers, 2 old managers and 1 new manager = 580 *15 = 8700

Therefore, the salary of the new manager is 9000 - 8700 = 300 less than that of the old manager who left the company, which is equal to 720 - 300 = 420.

Another alternate method of doing the problem is as follows:

The average salary dropped by Rs.20 for 15 of them. Therefore, the overall salary has dropped by 15*20 = 300.

Therefore, the new manager's salary should be Rs.300 less than that of the old manager = 720 - 300 = 420.