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

**Problem**

**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.

- 26
^{th}Day, A - 27
^{th}Day, A - 25
^{th}Day, B - 29
^{th}Day, B - 27
^{th}Day, B

**The Usual Method**

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Amount of work A finishes in 1 day = ,

Similarly, amount of work B finishes in 1 day =

Thus the amount of work finished in two consecutive days =

Hence total number of days needed to finish the work:

in 2 days means in 1 day.

Hence, days.

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

As can be seen, that since A started to work on the 1^{st} day and B on the 2^{nd} day and so on alternately, A will be working on all odd numbered days and B on all even numbered days. Thus on the 27^{th} 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 1^{st} day and B on the 2^{nd} 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 26^{th} 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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