A fort has provisions for 50 days. If after 10 days they are strengthened by 500 men and the food lasts for 35 days longer, the number of men originally in the fort were
(a)2500
(b)3000
(c)3500
(d)4000
Answer
Answer (as printed): C
Explanation
Let there be $x$ men originally. So, $x$ men had provisions for 40 days whereas $(x+500)$ men consumed it in 35 days. More men, Less days (Indirect Proportion). $\therefore (x+500):x::40:35 \Leftrightarrow 35(x+500) = 40x \Leftrightarrow 5x = 35 \times 500 \Leftrightarrow x = \frac{35 \times 500}{5} = 3500$.
Explanation as extracted from the printed page; notation may be imperfect.