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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 5

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

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

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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.

Using Technique

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Original ratio = 50 : 1

New ratio = 75 : 1

The additional 75 – 50 = 25 is attributable to the additional 500 agents. Hence, each unit or 1 corresponds to 500 / 25 = 20. Hence, 20 mangers and so option ‘3’.

(Ans: 3)

Estimated Time to arrive at the answer = 10 seconds.
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