Question

A garrison of $200$ men had provisions for $45$ days . After $15$ days , $40$ more men join the garrison. Find the number of days for which the remaining food will last.

Answer 1

$200$ men had provisions for $45$ days.

After $15$ days

$200$ men had provision for $30$ days.

Now

$\left(1\right)$ Number of men $\left(x_1\right)=200$

Provision finished $\left(y_1\right)=30$ day

$\left(2\right)$ After $15$ days number of men

joined all $40$

Therefore,

Number of men after $15$ days $\left(x_2\right)=240$

But food last in $42$ days

$x_2{y}_2=x_1{y}_1$

$y_2=\frac{200\times 30}{240}$

$=25$ days

Therefore remaining food will last in $25$ days.