Discussion Forum

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:

Explanation:

The problem becomes :

3300 men taking 850 gms per head have provisions for $(32-7)$ or 25 days. How many mei. taking 825 gms each have provisions for 17 days ?

Less ration per head, More men   (Indirect Proportion)

Less days, More men                       (Indirect Proportion) 

$\left\{\begin{array}{c}Ration\quad 825:850\\ Days\quad\quad 17:25\end{array}\right\}::3300:x$  

$825\times 17\times x$ $=850\times 25\times 3300$ or $x=\left(\frac{850\times 25\times 3300}{825\times 17}\right)$ = 5000

Strength of reinforcement $=(5500-3300)$ = 1700.