Question

A fort has provision for $50$ days. If after $10$ days they are strengthened by $500$ men and the food lasts $35$ days longer, how many men are there in the fort?

• A. $4000$
• B. $2500$
• C. $3500$
• D. $3000$

Answer 1

Answer: (C)

$3500$

Let there be $x$ men originally.

So, $x$ men had provisions $40$ days whereas $(x+500)$ men consumed it in $35$ days

Let us find the number of men in the fort as shown below:

$\frac{x+500}{x}=\frac{40}{35}\Rightarrow \frac{x+500}{x}=\frac{8}{7}\Rightarrow 7(x+500)=8x\Rightarrow 7x+3500=8x\Rightarrow 8x-7x=3500\Rightarrow x=3500$

Hence, there are $3500$ men in the fort.