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# [Smart Math] Ratio Proportion Problem 27

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

### Problem

A contractor undertakes to do a piece of work in 40 days. He engages 100 men and after 35 days, an additional 100 men and completes the work. How many days behind schedule would he have been, had he not engaged the additional men?

1. 5 days
2. 8 days
3. 12 days
4. 15 days
5. 18 days

### The Usual Method

Assume the total number of days taken be ‘x’, had the contractor not engaged additional men. Hence, $\frac{1}{x}$ of the work was done in 1 day.

So, 100 men working for 40 days will do $\frac{40}{x}$ of the work. But additional 100 men also work for 5 days. Hence, $\frac{5}{x}$ of the work is done by the additional men.

If $\frac{40}{x}$ of the work is done, the work remaining to be done = $\frac{x-40}{x}$.

This remaining work is done by the additional 100 men in 5 days.

Thus $\frac{x-40}{x}$ = $\frac{5}{x}$

$\therefore x-40=5$

$\therefore x=45$days.

Hence, had the contractor not brought in 100 additional men, the work would have been completed 45 – 40 = 5 days after its scheduled time.

(Ans: 1)

Estimated Time to arrive at the answer = 45 seconds.