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

**Problem**

**Problem**

A fort has a provision for 900 men for 40 days. After 20 days, 300 men join them. For how many days more will the provision last for?

- 5 days
- 10 days
- 15 days
- 20 days
- 25 days

**The Usual Method**

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Total provision is equivalent to 900 x 40 = 36,000 man days

Of this total, 900 x 20 = 18,000 man days worth of provision is already consumed in the first 20 days by the 900 men.

Hence balance provision is equivalent to 36,000 – 18,000 = 18,000 man days.

With 300 more men joining, total number of men in the fort = 900 + 300 = 1200 men.

Let ‘*x*’ be the number of days for which the provision would last from the day the 300 men joined in.

Hence total number of new man days = = man days.

This should be equivalent to 18,000 man days.

days

**(Ans: 3)**

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

**Using Technique**

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Since 20 days worth of provision is already consumed, the balance provision would last for 40 – 20 = 20 more days. Since 300 more men joining there is a % increase.

Hence to keep the total consumption constant, the number of days has to be reduced by 25%. (See concept explained in section of Percentage in Stuff to Remember)

A 25% reduction on the balance 20 days results in 20 – 5 = 15 days.

**(Ans: 3)**

*Estimated Time to arrive at the answer = 15 seconds.*

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