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. $29\frac{1}{5}$
• B. $37\frac{1}{4}$
• C. $42$
• D. $54$

Answer 1

The correct option is C $42$

After $10$ days: $150$ men had food for $35$ days.
Suppose $125$ men had food for $x$ days. Less men, More days; More men less days.
$\therefore$ $125:150::35:x$
$\Rightarrow 125\times x=150\times 35$
$\Rightarrow x=\frac{150\times 35}{125}\Rightarrow x=42$