Question

A fort had provisions for 150 men for 50 days. After 15 days, 25 men left the fort. How long will food last at the same rate for remaining men? $\left[2\text{Marks}\right]$

Answer 1

Let required number of days that the food lasts be $‘x^{\prime }$. Here the number of men are reduced so the food will last longer. It is a case of inverse variation.
Now, after 15 days the remaining food will last for (150 - 25) = 125 men. (0.5 mark)
So, the amount of food which would last for the 125 men in the remaining days should be equal to the amount of food that lasts for 150 men for 50 - 15 = 35 days.

$\frac{150}{125}$ $=\frac{x}{35}$

$x=\frac{150\times 35}{125}=42days$. (1.5 marks)