Question

A garrison of 200 men had enough food for 70 days. 80 men went away after 10 days. How long will the remaining food last?

• A. 100 days
• B. 110 days
• C. 120 days
• D. 90 days

Answer 1

The correct option is A 100 days

After 10 days there were enough food for 60 days, but the number the garrison is reduced to (200 - 80) = 120 days

The remaining food lasts for x days (say)

Ratio of the supposed no. of days to the new number of days $=\left(\frac{60}{x}\right)$

Now, the number of men being less than the original member, the food will last for more days. Number of men is inversely proportional to the number of days the food lasts.
$\left(\frac{Reducednumberofmen}{Originalno.ofmen}\right)=\frac{(No.ofdaysthefoodlastsoriginally)}{(No.ofdaysthefoodlastsfortheremainingperson)}$
$\left(\frac{120}{200}\right)=\left(\frac{60}{x}\right)$
Or, 120x = 200 $\times$ 60
Or, x = 100 days