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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 20

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

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

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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.

Using Technique

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It takes 1 boy 12 days to finish the work, so it will take 12 boys to finish the work in 1 day. Also, 3 men = 4 women = 12 boys.
Thus 1 man = 4 boys and 1 woman = 3 boys.
Thus if 12 boys are needed to finish the work in 1 day, if 1 man and 1 woman are working together, they will do the work of 4 + 3 = 7 boys. Hence, balance number of boys i.e. 12 – 7 = 5 will be needed to finish the work in 1 day.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.
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