Question

1600 soldiers in a camp had enough food for 30 days . after 8 days , some soldiers left the camp and thus the food lasted for another 32days. how many soldiers left the camp ?​

Answer 1

$\sf\large\underline\red{Let:-}$

$\sf{\implies Number\:_{(left\: soldiers)}=x}$

$\sf\large\underline\red{Given:-}$

$\sf{\implies Number\:_{(soldiers\:in\:camp)}=1600}$

$\sf{\implies Food\: enough\:_{(for\: soldiers)}=30\:days}$

$\sf\large\underline\red{To\:Find:-}$

$\sf{\implies Number\:_{(left\: soldiers)}=?}$

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

To calculate the number of left soldiers in the camp , at first we have to focus on the given Question. As given in the question that 1600 soldiers had enough food for 30 days but after 8 says some soldiers left the camp and as some soldiers left the camp then the food enough for the soldiers for 32 days. It means here we have to decrease the days and number of soldiers and left soldiers so, the remaining days for the soldiers is 30-8=22days and the remaining soldiers is 1600-x. By setting up equation we can easily find the number of left soldiers from the camp.

$\sf{\implies Left\: soldiers*32\:days=Total\: soldiers*22days}$

$\tt{\implies (1600-x)*32=1600*22}$

$\tt{\implies 51200-32x=35200}$

$\tt{\implies -32x=35200-51200}$

$\tt{\implies -32x=-16000}$

$\tt{\implies 32x=16000}$

$\tt{\implies x=500}$

$\sf\large{Hence,}$

$\sf{\implies Number\:_{(left\: soldiers)}=500}$

Answer 2

Question:-

1600 soldiers in a camp had enough food for 30 days . after 8 days , some soldiers left the camp and thus the food lasted for another 32 days. How many soldiers left the camp ?

Solution:-

Given that there are 1600 soldiers in the camp.

Also it is given that after 8 days out of the given 30 days, the camp has enough food for 1600 soldiers.

That is for 30-8=22 days, the camp has enough food.

Let the number of soldiers left this camp be ‘X’.

Number of soldiers left in the camp = (1600 – X)

Given that the food remains for 32 days

Number of soldiers 1600 lasted for 22 days.

Number of soldiers 1600-X lasted for 32 days.

Clearly notice that the two quantities are in inverse proportion.

⇒ 1600 x 22 = (1600-X) x 32

⇒ 35200=51200-32X

⇒32X=51200-35200

⇒32X=16000

⇒X=16000/32

⇒X=500

Thus the number of soldiers left is 500