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# [Smart Math] Ratio Proportion Problem 11

Here’s and example of a SMART MATH problem for 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

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.