Question

camp had provisions for 490 soldiers for 65 days. After 15 days, more soldiers arrived
and the remaining provisions lasted for 35 days. How many soldiers joined the camp​

Answer 1

210 soldiers

Explanation:

Number of soldiers = 490

Number of days = 65

After 15 days,

Number of soldiers = 490

Number of days = 65 – 15 = 50

After 15 days, more soldiers arrived. Let x be the more soldiers.

Number of soldiers = 490 + x

Number of days = 35

Soldiers        Days

   490              50

490 + x            35

Here as the soldiers increased the food last for less days.

Therefore, it is inverse proportion.

The proportion is $(490+x): 490: 50: 35$

Product of extremes = product of means

$\Rightarrow (490+x) \times 35=490 \times 50$

$\Rightarrow(490+x)=\frac{490 \times 50}{35}$

$\Rightarrow(490+x)=700$

$\Rightarrow x=700 -490$

$\Rightarrow x=210$

Therefore, 210 soldiers joined the camp.