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

✬ Soldiers = 300 ✬

Step-by-step explanation:

Given:

• Total number of soldiers in fort is 1200.
• For 1200 soldiers food is enough for 28 days.
• After 4 days some soldiers transferred to another fort.
• Now food will last for extra 32 days.

To Find:

• How many soldiers left the fort ?

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

• For 1200 soldiers food will last after 28 days.

• But after 4 days some of them left the fort. Therefore

∴ Now food will last after 28 – 4 = 24 day.

➮ Number of remaining soldiers

• 1200 – Left
• (1200 – x) soldiers are now in fort.

A/q

• For remaining soldiers food will last after 21 days.

• No. of soldiers = 1200ㅤ,1200 – x
• Food last after = 24 ㅤ,ㅤ32

• This is in the form of inverse variation.

$\implies{\rm }$ 1200 × 24 = (1200 – x)32

$\implies{\rm }$ 28800 = 38400 – 32x

$\implies{\rm }$ 28800 – 38400 = – 32x

$\implies{\rm }$ – 9600 = – 32x

$\implies{\rm }$ 9600/32 = x

$\implies{\rm }$ 300 = x

Hence, 300 soldiers left the fort.

Answer 2

Answer:

➡️ Solution ⬅️

$\leadsto$ Let the number of soldiers left = x

⚜️ After 4 days, for 1200 soldiers the food would last for = 28-4=24 days

✝️ Now we have the food that would last for 1200 soldiers= 24 days and for 1200-x soldiers = 32 days

✳️When the number of soldiers decrease, the food would last for more days. thus there is inverse variation between soldeirs and number of days.

$\mapsto$ Therefore we get,

⇒1200×24=(1200−x)×32

⇒x=300

✔️ Thus the number of soldiers left the fort is 300.

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