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# [Smart Math] Ratio Proportion Problem 5

Here’s and example of a SMART MATH problem for RATIO PROPORTION.

### Problem

In a Call Center the ratio of agents to manager is 50 : 1. If 500 more agents join, the ratio changes to 75 : 1. How many managers are there?

1. 30
2. 25
3. 20
4. 15
5. 10

### The Usual Method

If there are ‘x’ managers; the total number of agents initially are 50x.

Thus, new set of agents = 50x + 500

$\therefore \frac{50x+500}{x}=\frac{75}{1}$

$\therefore 75x=50x+500$

$\therefore 25x=500$

$\therefore x=\frac{500}{25}=20$

(Ans: 3)

Estimated Time to arrive at the answer = 60 seconds.