Question

A fort had provisions for 150 men for 45 days. After 10 days 25 men leave the fort.
How long will the food last at the same rate?
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Answer 1

Answer :

42 days.

Explanation :

In a fort,

Food provision for 150 men is for 45 days.

After 10 days 25 men left the fort

∴ Number of days left = 45 - 10 = 35 days.

∴ Number of men remains = 150 - 25 = 125 men

Now, the provision for 150 men is of 35 days.

We need to find out for 125 men.

Let's say the food provision for 125 men will last for $x$ days.

Since, number of men decreases, the number of days will increase.

∴ It's an inverse proportion.

Doing proportional analysis :

$\implies 150 \times 35 = 125 \times x$

Solving for $\boldsymbol{x \: :}$

$\implies \dfrac{150 \times 35}{125} = {x}$

$\implies x = 42$

∴ Required answer : 42 days.