Question

5) A garrison of 1400 men has provisions for 36 days. But due to arrival of reinforcements, the provisions could last for only 28 days. How many more men joined the garrison?

Answer 1

Answer is 400. Please check the image for the solution!

Answer 2

Given,

There are 1400 men in a garrison, with provisions for 36 days.

To Find,

The number of men who came as reinforcement, such that the provision lasts for only 28 days.

Solution,

Let us say the consumption by 1400 men per day = $x$

Thus the total consumption in 36 days = $1400$ × $36$ ×$x$

Now since the total consumption is to be completed in 28 days,

⇒ $1400$ × $36$ × $x = (1400 + n)$ × $28$ × $x$

⇒ $1400$ × $36 =$ $(1400 + n)$ × $28$

⇒ 1400 + n = $\frac{50400}{28}$ $= 1800$

⇒ n = 1800 - 1400 = 400

Henceforth 400 men had arrived as reinforcement.