Question

6. In a camp with 64 soldiers, there is enough
ammunition to last for 16 days. If after 2 days,
8 soldiers leave the camp, for how long will the
ammunition last?​

Answer 1

For 64 soldiers, ammunition last for 16 days.

After 2 days, 8 soldiers left.

Remaining soldiers = 56.

Now, for 64 soldiers the ammunition is to last for 14 days(2 days being completed)

But there are only 56 soldiers and hence the ammunition is to last for more days(more than 14)

64*14 days = 56*x days

x = 64*14/56 = 16

Hence the ammunition will last for another 16 days.

Answer 2

For 64 soldiers , ammunition lasts for 16 days

So, for 1 soldier, ammunition lasts for (16 * 64)days

Therefore,

in 1 day ammunition consumed by 1 soldier

= 1/(16*64)

Ammunition consumed by 64 soldiers in 2 days

= (2*64)/(16*64)

= 1/8

Ammunition left now

= 1 - (1/8)

= 7/8

Soldiers left after 2 days = 64-8 = 56

Ammunition consumed by 56 soldiers in 1 day

= 56/(16*64)

= 7/128

Therefore,

Days for which remaining ammunition will last

= (7/8) /(7/128)

= 16 days