Question

1200 soldiers in a fort had enough food for 28 days. After 4 days, some soldiers were transferred to another fort and thus the food lasted for an extra 32 days. How many soldiers left the fort? ​

Answer 1

Answer:

It is given that after 4 days, out of 28 days, the fort had enough food for 1200 soldiers for (28−4=24) days.

Let x be the number of soldiers who left the fort.

Number of soldiers 1200 1200−x

Number of days for which food lasts 24 32

Since, the number of soldiers and the number of days for which the food lasts are in inverse variation, we have :

⇒ 1200×24=(1200−x)×32

⇒

32

1200×24

=1200−x

⇒ 900=1200−x

⇒ x=1200−900

⇒ x=300

∴ The soldiers which left the fort are 300.