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

**Problem**

**Problem**

3 men and 6 women can dig a well in 4 days. 5 men and 4 women take 3 days. How many days would 8 women and 1 man take?

- 6 days
- 8 days
- 10 days
- 4 days
- 9 days

**The Usual Method**

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Let ‘m’ be the fraction be the amount of work done by 1 man in 1 day and ‘w’ be the fraction of work done by 1 woman in 1 day.

3m + 6w = 1/4

12 m + 24 w = 1 …… Eq. 1.

Similarly, 5m + 4w = 1/3

15m + 12w = 1 …… Eq. 2.

Solving both equation 1 and 2 simultaneously we get

18m = 1 and 72w = 1

m = and w =

8w + 1m =

Hence, 6 days.

**(Ans: 1)**

*Estimated Time to arrive at the answer = 120 seconds.*

**Using Technique**

** **

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If 3 men and 6 women take 4 days, hypothetically, 1.5 men and 3 women will take 8 days. Hence, 1 man and 8 women will obviously take less than 8 days. Also, 1 man and 8 women will also take more than 4 days; hence the answer lies between 8 days and 4 days i.e. 6 days.

** **

**(Ans: 1)**

*Estimated Time to arrive at the answer = 5 seconds.*

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