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# [Smart Math] Ratio Proportion Problem 58

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

### 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?

1. 5 days
2. 10 days
3. 15 days
4. 20 days
5. 25 days

### The Usual Method

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 = $1200\times x$ = $1200x$ man days.

This should be equivalent to 18,000 man days.

$\therefore 1200x=18000$

$\therefore x=\frac{18000}{1200}=15$days

(Ans: 3)

Estimated Time to arrive at the answer = 45 seconds.

### Using Technique

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 $\frac{300}{900}\times 100=33.33$% increase.