Question

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. For how many days the remaining food will last?
A.$29\dfrac{1}{5}$
B.$37\dfrac{1}{4}$
C.42
D.54

Answer 1

Hint- We approach this question in such a way that we know in the start 150 men had food for 45 days. After the passage of 10 days 150 men still had food for 35 days but since 25 men left the fort so we can say that only 125 men are left in the fort. We will suppose the food be last for x days for the 125 men and then we will just use the indirect proportion technique because we know that less men, more days for the food to last and on simplifying the ratios we get the required number of days for which the food will last for 125 men after 10 days.
Complete step-by-step answer:
It is given that 150 men had food for 45 days.
After 10 days, 150 men still had food for 35 days.
Since, 25 men left the fort so $150 - 25 = 125$ men are left in the fort.
Now, let us suppose that 125 men had food for the x number of days.
We know that we have the case of indirect proportion here because as the number of men will decrease food will last for a greater number of days.
$ \Rightarrow 125:150::35:x$ or $\dfrac{{125}}{{150}} = \dfrac{{35}}{x}$
$ \Rightarrow 125 \times x = 35 \times 150$
$ \Rightarrow x = \dfrac{{5250}}{{125}}$
$ \Rightarrow x = 42$
Hence, we can say that the 125 men had food for the x = 42 days.
$\therefore $ Option C. 42 is the correct answer

Note- For such types of questions, just keep in mind the concept of inverse proportion that when one value decreases then the other value increases at the same rate. Likewise, as the number of men will decrease, food will last for a greater number of days. Also, do the comparisons very carefully in such types of questions.