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# [Smart Math] Ratio Proportion Problem 20

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

### Problem

A man, a woman or a boy can do a piece of work in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to finish the work in 1 day?

1. 3
2. 5
3. 6
4. 7
5. 8

### The Usual Method

Amount of work done by 1 man in 1 day = $\frac{1}{3}$
Amount of work done by 1 woman in 1 day = $\frac{1}{4}$
Amount of work done by 1 man and 1 woman working together for 1 day = $\frac{1}{3}+\frac{1}{4}=\frac{7}{12}$
Hence, amount of work yet to be done = $1-\frac{7}{12}=\frac{5}{12}$
Amount of work done by 1 boy in 1 day = $\frac{1}{12}$
Hence, it will take 5 days for one boy or 1 day for 5 boys to finish the work.

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.