Question

A port had provisions for $450$ men for $80$ days. After$10$ days $50$ more men arrived. How long will the remaining food last at the same rate?

Answer 1

No. of men at the beginning $=450$

No. of men arrived after $10$ days $=50$

Total Number of mens after $10$ days $=450+50=500$

Total . of days $=80$

After $10$ days, period $=70$ days

After $10$ days, there will be $500$ mens

Let $x$ be the no. of days till which the food remains

$\therefore 450:500=70:x$

By inverse proportion,

$500:450=70:x$

$⟹\frac{500}{450}=\frac{70}{x}$

$⟹x=\frac{70\times 450}{500}$

$⟹x=63$

Hence, till $63$ days, the remaining food lasts at the same rate.