Question

a Garrison had provision for 520 men to last for 27 days how many men must be transferred to another Garrison to that the same food last for 30 days​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

A garrison had provision for 520 men to last for 27 days.

Now, we have to find how many men must be transferred to another garrison so that the same food last for 30 days.

Let assume that x men be transferred to another garrison.

As we know, if number of men is less, the provision of food is more for number of days.

So, number of men and number of days are in indirect variation.

So, we have garrison had provision for 520 men to last for 27 days. Now, garrison had provision for 520 - x men to last for 30 days.

So,

$\begin{array}{|c|c|c|c} \hline \rm Number \: of \: men&\rm 520&\rm 520 - x \\ \hline\rm Number \: of \: days&\rm 27&\rm 30 \\ \hline \end{array}$

So, using Law of indirect variation, we have

$\rm \: 520 \times 27 = (520 - x) \times 30$

$\rm \: 520 \times 9 = (520 - x) \times 10$

$\rm \: 520 \times 9 = 520 \times 10 - 10x$

$\rm \: 10x= 520 \times 10 - 520 \times 9$

$\rm \: 10x= 520 \times (10 - 9)$

$\rm \: 10x= 520 \times 1$

$\rm \: 10x= 520$

$\rm\implies \:x = 52$

So, 52 men must be transferred to another garrison so that the same food last for 30 days.