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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 29

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

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

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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.

Using Technique

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Since, the 7 men work for 2 weeks, balance work is equivalent of 14 – 2 = 12 weeks. However, now since 7 more men join, the capacity doubles up and so time required halves. Hence, time taken will be half of 12 weeks = 6 weeks.

(Ans: 2)

Estimated Time to arrive at the answer = 10 seconds.
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