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

**Problem**

**Problem**

A certain number of men can finish a piece of work in 100 days. If however, there were 10 men less, it would take 10 days more to finish the work. How many men were there originally?

- 50
- 75
- 82
- 100
- 110

**The Usual Method**

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Let the original number of men = *x*.

Hence, if *x* men take 100 days to finish the work, 1 man will take 100*x* days.

Also, by having 10 men less, the number of men becomes (*x* – 10) and the number of days becomes 100 + 10 = 110 days. Thus 1 man working alone will take days.

This is equal to 100*x* days.

men

**(Ans: 5)**

*Estimated Time to arrive at the answer = 60 seconds.*

**Using Technique**

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Assuming that there are 100 men working for 100 days, hence total work is for 10,000 man-days. With a reduction in number of men to 90, days increase to 110. Hence, work is equivalent to 90 x 110 = 9900 man-days. This is slightly less than 10,000 man-days. Hence, the actual number of men should be slightly greater than 100. As per the options, the only option slightly greater than 100 is 110.

**(Ans: 5)**

*Estimated Time to arrive at the answer = 15 seconds.*

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