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

**Problem**

**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?

- 20 days
- 30 days
- 40 days
- 50 days
- 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* =

Also, if B does half of what A and C do in a day,

Or

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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