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1. 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

Solution:

Let the remaining food last for x days
500 men had provision for = (27 - 3) = 24 days
(500 + 300) men had provision for x days
More men, Less days (Indirect proportion)

\begin{aligned} ∴ 800 : 500 :: 24 : x \\ \Leftrightarrow (800 \times x) = (500 \times 24) \\ \Leftrightarrow x = \frac{(500 \times 24)}{800} \\ \Leftrightarrow x = 15 \end{aligned}

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