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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 11

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

Ratio Proportion

Problem

A can do a piece of work in 20 days and B in 40 days. A begins the work and there after A and B work on alternate days, the work then finishes during the course of the ________ day when ___________ is working.

  1. 26th Day, A
  2. 27th Day, A
  3. 25th Day, B
  4. 29th Day, B
  5. 27th Day, B

The Usual Method

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Amount of work A finishes in 1 day = \frac{1}{20},

Similarly, amount of work B finishes in 1 day = \frac{1}{40}

Thus the amount of work finished in two consecutive days = \frac{1}{20}+\frac{1}{40}=\frac{3}{40}

Hence total number of days needed to finish the work:

\frac{3}{40} in 2 days means \frac{3}{80} in 1 day.

Hence, \frac{80}{3}=26\frac{2}{3} days.

Thus it will be the 27th day on which the work will finish.

As can be seen, that since A started to work on the 1st day and B on the 2nd day and so on alternately, A will be working on all odd numbered days and B on all even numbered days. Thus on the 27th Day, A will be working.

(Ans: 2)

Estimated Time to arrive at the answer = 60 seconds.

Using Technique

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Since, A works on the 1st day and B on the 2nd and so on alternately, A will be working only on odd numbered days. Thus, option ‘1’ can be eliminated since A cannot work on the 26th day. Similarly, options ‘3’, ‘4’ and ‘5’ can also be eliminated since B works only on even numbered days. This leaves us only with the options ‘2’.

(Ans: 2)

Estimated Time to arrive at the answer = 5 seconds.
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