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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 4

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

Ratio Proportion

Problem

3 men and 6 women can dig a well in 4 days. 5 men and 4 women take 3 days. How many days would 8 women and 1 man take?

  1. 6 days
  2. 8 days
  3. 10 days
  4. 4 days
  5. 9 days

The Usual Method

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Let ‘m’ be the fraction be the amount of work done by 1 man in 1 day and ‘w’ be the fraction of work done by 1 woman in 1 day.

\therefore 3m + 6w = 1/4

\therefore 12 m + 24 w = 1                                       …… Eq. 1.

Similarly, 5m + 4w = 1/3

\therefore 15m + 12w = 1                                         …… Eq. 2.

Solving both equation 1 and 2 simultaneously we get

18m = 1 and 72w = 1

\therefore m = \frac{1}{18} and w = \frac{1}{72}

\therefore 8w + 1m = \frac{8}{72} + \frac{1}{18} = \frac{3}{18} = \frac{1}{6}

Hence, 6 days.

(Ans: 1)

Estimated Time to arrive at the answer = 120 seconds.

Using Technique

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If 3 men and 6 women take 4 days, hypothetically, 1.5 men and 3 women will take 8 days. Hence, 1 man and 8 women will obviously take less than 8 days. Also, 1 man and 8 women will also take more than 4 days; hence the answer lies between 8 days and 4 days i.e. 6 days.

(Ans: 1)

Estimated Time to arrive at the answer = 5 seconds.
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