A garrison of 3300 men had provisions for 32 days, when given at the rate of 850 gms per head. At the end of 7 days, a reinforcement arrives and it was found that the provisions will last 17 days more, when given at the rate of 825 gms per head. What is the strength of the reinforcement?
Answer
Answer (as printed):
Explanation
The problem becomes: 3300 men taking 850 gms per head have provisions for $(32-7)$ or 25 days. How many men taking 825 gms each have provisions for 17 days? Less ration per head, More men (Indirect Proportion). Less days, More men (Indirect Proportion). Ration $825:850$, Days $17:25$ :: $3300:x$. $\therefore 825 \times 17 \times x = 850 \times 25 \times 3300$ or $x = \frac{850 \times 25 \times 3300}{825 \times 17} = 5000$. $\therefore$ Strength of reinforcement $= (5000-3300) = 1700$.
Explanation as extracted from the printed page; notation may be imperfect.