A garrison of 500 men had provisions 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
Answer (as printed): A
Explanation
Let the remaining food 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 (Indirect Proportion). $\therefore 800:500::24:x \Leftrightarrow (800 \times x) = (500 \times 24) \Leftrightarrow x = \frac{500 \times 24}{800} = 15$.
Explanation as extracted from the printed page; notation may be imperfect.