Question

a garrison of 120 men has provision for 30 days . at the end of 5 days, 5more men joined them. how many days can they sustain on the remaining provision?

Answer 1

we know that no. of days is inversely propotional to the provision for men. 

So for 120 men the provision would last for 30days. (given) 

Therefore, the provision for 1 men would sustain for. 120 *30 = 3600 days. 

Let after the joining of 5 men (after 5 days) the no of more days the provision would last is x days 

A.t.q 120*30 = 120*5+125*x 

(120*30) - (120*5)= 125x 

120(30-5)=125x 

120 * 25 = 125x 

120 = 5x 

x=120/5 

x= 24 

so the provision would remain for more 24 days.

Answer 2

Given that,

Number of men = 120

Time = 30 days

At the end of 5 days, 5 more men joined them.

For 120 men there is provision for 30 days

If 1 man needs 1 unit of provision in a day

Then, total provision = $120\times30$

Total provision =3600

120 men in 5 days will take = $120\times5$

120 men in 5 days will take = 600 unit of provision

Remaining provision = 3600-600

Remaining provision =3000 units

5 more men joined and now there are total 125 men

We need to calculate the days on the remaining provision

1 day provision requirement for 125 men = 125 units

Days for which they can sustain on remaining provision =$\dfrac{3000}{125}$

Days for which they can sustain on remaining provision =24 days

Hence, They can sustain on remaining provision for 24 days.