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# [Smart Math] Ratio Proportion Problem 29

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

### Problem

7 men can dig a canal in 14 weeks. After 2 weeks of work, they are joined by another 7 men. In how many weeks more is the work finished?

1. 5
2. 6
3. 8
4. 9
5. 11

### The Usual Method

If 7 men can dig a canal in 14 weeks, than 7 men can dig $\frac{1}{14}$th of the canal in 1 week. Since, 7 men work for 2 weeks, $\frac{2}{14}$ or $\frac{1}{7}$th of the canal is dug. Hence, amount of work remaining = $\frac{6}{7}$.

Additional 7 men join, so now it becomes 14 men. If 7 men dig a canal in 14weeks, 14 men will take 7 weeks to dig the canal. Hence, $\frac{1}{7}$th of the canal will be dug by 14 men in 1 week.

Since it takes 1 week to do $\frac{1}{7}$ of the work, to do $\frac{6}{7}$ of the work, it will take 6 weeks.

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.