Question

A fort had provisions for $300$ men for $90$ days. After $20$ days, $50$ men left the fort. How long would the food last at the same rate?

• A. $62$
• B. $84$
• C. $56$
• D. $72$

Answer 1

The correct option is B $84$

Remaining number of men $=(300-50)=250$.
Remaining number of days $=(90-20)days=70$ days
300 men had provisions for $70$ days
1 man had provisions for $(300\times 70)$ days ...[less men, more days]
$250$ men had provisions for $\frac{300\times 70}{250}$ days $=84$ days ...[more men, less days]
Hence, the remaining food will last for $84$ days.