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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 12

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

Ratio Proportion

Problem

A, B and C can together complete a piece of work in 10 days. If B does half of what A and C do in 1 day, in how many days can B alone finish the work?

  1. 20 days
  2. 30 days
  3. 40 days
  4. 50 days
  5. cannot be determined

The Usual Method

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Let the amount of work that A, B and C do individually per day be ‘1’, ‘2’ and ‘3’.

Then a + b + c = the amount of work done in 1 day.

Since, it takes 10 days to finish the work, a + b + c = \frac{1}{10}

Also, if B does half of what A and C do in a day, b=\frac{1}{2}(a+c)

Or 2b=a+c

\therefore a+b+c=\frac{1}{10}

=b+2b=\frac{1}{10}

\therefore 3b=\frac{1}{10}

\therefore b=\frac{1}{30}

Hence, B alone would take 30 days to finish the work.

(Ans: 2)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Assuming A and C together as a new person D, then we can say that B and D together finish the work in 10 days. Also, B is half as efficient as D. In other words, D has double the efficiency than B and so can do double the work that B can do in the same time. Hence, if the work is divided in 3 parts, D will do 2 parts of the work and 1 part would be done by B.

Hence, the ratio of total work, to the amount of work done by B alone is 3 : 1.Hence, the ratio of the number of days, it takes to finish the work by working together to that taken by B working alone will be 1 : 3. Since, if efficiency decreases, the number of days took increase in the same proportion. Hence, number of days taken by B alone will be 10 x 3 = 30 days.

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds.
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