Question

A garrison of $120$ men has provision for $30$ day. At the end of five days, five more men joined them. How many days can they sustain on the remaining provision?

Answer 1

Let after the joining of $5$ men (after 5 days), It took $x$ days to sustain on the remaining provision then,

According to the question-

Total food consumed in $30$ days = Food consumed by 120 men in $5$ days $+$ Food consumed by $125(120+5)$ men in the remaining $x$ days

$\Rightarrow 120\times 30=120\times 5+125\times x$

$\Rightarrow (120\times 30)-(120\times 5)=125x$

$\Rightarrow 120(30-5)=125x$ [Using Distributive Property]

$\Rightarrow 120\times 25=125x$

$\Rightarrow 120=5x$

$\Rightarrow x=24$days

Hence, for 24 days they can sustain on the food available.