Question

A fort had provision of food for 150 men for 45 days. After 10 days 25 men left the fort. The number of days for which the remaining food will last is____.
(a) $29\dfrac{1}{5}$
(b) $37\dfrac{1}{4}$
(c) $42$
(d) $54$

Answer 1

Hint: In this question, food provision is provided for 150 men in 45 days. After 25 men left the fort, the total number of men in the fort was 125. So, let the food accumulated be ‘x’. Now, equating today’s food accumulation which is 125x with earlier food accumulation, we can easily calculate the number of days for which food will last.

Complete step-by-step answer:
We use the concept of Indirect proportion i.e. “Two quantities a and b are said to be in indirect proportion if an increase in the quantity a, there will be a decrease in the quantity b, and vice-versa. In other words, the product of their corresponding values should remain constant.”
We let the number days be ‘x’. The fort had provision of food for 150 men for 45 days. After 10 days as given in the question, 25 men left the fort, so 125 men are there in the fort. So, the fort has food for 150 men for 35 days. But there are 125 men in the fort.
Now, we calculate the number of days for which the remaining food will last:
Let, 125 men have food for ‘x’ days.
Now,
According to the law of indirect proportion, there are less men so more day’s food.
\[\begin{array}{*{35}{l}}
   \begin{align}
  & 125\times x=150\times 35 \\
 & x=\dfrac{150\times 35}{125} \\
 & x=\dfrac{6}{5}\times 35 \\
 & x=6\times 7 \\
\end{align} \\
   x=42days \\
\end{array}\]
Hence, the number of days for which the remaining food will last is 42 days.
Therefore, option (c) is correct.

Note: The key concept for solving this question is the knowledge of law of indirect proportion. Students must remember that the food provision will remain the same (150) because food capacity is the same. But since some people left the food will last for a longer period of time. So, the food prepared should not be altered to obtain the correct result.