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# [Smart Math] Ratio Proportion Problem 23

Here’s and example of a SMART MATH problem for 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

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.