Problem Solving

A garrison of 750 men has provision for 20 weeks, if at the end of 4 weeks, they are reinforced by 450 men, how long the provision will last?


OA is 10 weeks

someone explain!

Let provision for 750 men for 20 weeks = x

Provision for 1 man for 1 week = x/(20*750)

Provision for 750 men for 1 week = x/20

Provision used up in first 4 weeks = 4* x/20 = x/5

Provision remaining = x - x/5 = 4x/5

Men added = 450. So, total men now = 750 + 450 = 1200

Provision for 1200 men for 1 week
= 1200 * x/(20*750) = 2x/25

Therefore no of weeks provision will last
= (4x/5)/(2x/25)
= 10 weeks

fruti_yum wrote:A garrison of 750 men has provision for 20 weeks, if at the end of 4 weeks, they are reinforced by 450 men, how long the provision will last?


OA is 10 weeks

someone explain!

Total provision is 750*20 =15,000
Provision used in 4 weeks is 750*4 =3,000
Provisions left = 15,000-3,000 = 12,000 ---(1)
Number of men is 750+450 = 1200---(2)

Eqn 1/ Eqn 2 gives 10

Thanksm
Quant-Master

fruti_yum wrote:A garrison of 750 men has provision for 20 weeks, if at the end of 4 weeks, they are reinforced by 450 men, how long the provision will last?


OA is 10 weeks

someone explain!