Question

A garrison of $500$ men had provision for $27$ days. After $3$ days a reinforcement of $300$ men arrived. For how many more days will the remaining food last now?

• A. $15$
• B. $16$
• C. $17\frac{1}{2}$
• D. $18$

Answer 1

The correct option is A $15$

Let'the remaining food will last for x days. 500 men had provisions for $(27-3)=24$ days. $(500+300)$ men had provisions for $x$ days. More men, less days
$\therefore$ $800:500::24:x$
$\Rightarrow 800\times x=500\times 24$
$\Rightarrow x=\frac{500\times 24}{800}=15$