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

**Problem**

**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.

- 9
- 10
- 15
- 21
- 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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