question_answer

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

Answer:

(a) Since, the remaining days\[=\left( 9020 \right)\] days = 70 days But remaining number of men \[=\text{ }30050\] = 250 Let the number of days = x, then

Number of men	300	250
Number of days	70	x

Clearly less men will have food for more days. Then, by inverse variation, \[\frac{300}{250}=\frac{x}{70}\] \[x=\frac{70\times 300}{250}\] \[x=\frac{70\times 6}{5}\] \[x=14\times 6\] = 84 Hence, the number of days = 84.