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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 54

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

Ratio Proportion

Problem

In equal amounts of time three professors are able to solve problems in the ratio of 1.5 : 2.5 : 3.5. If the professor with the least capability can solve 6 problems in 2 hours, how many problems will the professor with highest ability solve in 3 hours? Assume that they solve problems with uniform speed.

  1. 9
  2. 10
  3. 15
  4. 21
  5. 24

The Usual Method

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The ratio of solving problems is 1.5 : 2.5 : 3.5 or 3 : 5 : 7.

Also if the professor with least capability can solve 6 problems in 2 hours, he can solve 3 problems in 1 hour.

Thus from the ratio, the professor with highest capability can solve 7 problems in 1 hour. Hence in 3 hours the professor solves 7 x 3 = 21 problems.

(Ans: 4)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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The ratio of solving problems = 3 : 5 : 7, with 7 being the proportion of problems solved by the best professor. Thus the number of problems he solves should be a multiple of 7. This condition is met by option ‘4’ alone.

(Ans: 4)

Estimated Time to arrive at the answer = 5 seconds.
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