Question

A fort is provisioned for $42$ days. After $10$ days, a reinforcement of $200$ men arrives and the food will now last only $24$ days. How many men were there in the fort?

• A. $200$
• B. $600$
• C. $500$
• D. $300$

Answer 1

The correct option is B $600$

Let $x$ soldiers had provision for $42$ days in a fort.

After $10$ days: $x$ soldiers will remain with $32$ days of provision

therefore for $(x+200)$ soldiers provision will decrease to $24$ days

therefore By inverse proportion,

$x\times 32=(200+x)\times 24$

$\therefore \frac{32}{24}=\frac{200+x}{x}$

$\therefore \frac{32}{24}=\frac{200}{x}+1$

$\therefore \frac{32}{24}-1=\frac{200}{x}$

$\therefore \frac{8}{24}=\frac{200}{x}$

$\therefore x=\frac{200\times 24}{8}$

$\therefore x=600$

Answer is $600$ days