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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 6

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

Ratio Proportion

Problem

A can do a piece of work in 12 days. A and B together do the work in 8 days. How long would B alone take to complete the work?

  1. 8 days
  2. 10 days
  3. 15 days
  4. 18 days
  5. 24 days

The Usual Method

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A in one day will finish \frac{1}{12}th of the work.

Let B finish \frac{1}{b}th of the work in one day.

Hence, \frac{1}{12}+\frac{1}{b}=\frac{1}{8}

\therefore 8(b+12)=12b

\therefore 18b+96=12b

\therefore 4b=96

\therefore b=24 Days

(Ans: 5)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Should B take 12 days working alone, than A and B working together would take 6 days. But A and B together actually take 8 days; hence B would take more than 12 days to finish the work working alone. This eliminates options ‘1’ and ‘2’

Also note that the difference between 6 days and actual 8 days is that of 2 days. Simply multiplying 2 with 12 we get 24 days which is the answer.

(Ans: 5)

Estimated Time to arrive at the answer = 10 seconds.
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