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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 23

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

Ratio Proportion

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?

  1. 50
  2. 75
  3. 82
  4. 100
  5. 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 100x 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 (x-10)\times 110 days.

This is equal to 100x days.

\therefore (x-10)\times 110=100x

\therefore 110x-1100=100x

\therefore 10x=1100

\therefore x=110 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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