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

**Problem**

**Problem**

R can do a piece of work in 20 days and K in 25 days. They work together for 5 days and then K leaves. In how many days would R finish the work?

- 5
- 9
- 10
- 11
- 12

**The Usual Method**

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R can finish of the work in 1 day.

K can finish of the work in 1 day.

Thus total work finished by R and K working together for 5 days = .

Hence remaining work = .

Since R has to work alone now and R can finish of the work in 1 day, so for R to finish of the work, it will take,

1

*x*

By cross multiplication, we get:

11 days more.

**(Ans: 4)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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R will finish or 25% of the work in 5 days. K will finish or 20% of the work in 5 days. So, work remaining to be done = 100% – (25% + 20%) = 55%.

Since R takes 5 days to finish 25% of the work, he will take 10 days to finish 50% of the work. So for 55%, R will take a little over 10 days, so 11 days to finish. (Also, 55% is a multiple of 11, so the answer should also be a multiple of 11.)

**(Ans: 4)**

*Estimated Time to arrive at the answer = 10 seconds.*

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