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In a barrack of soldiers there was stock of food for 190 days for 4000

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Bunuel
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In a barrack of soldiers there was stock of food for 190 days for 4000 [#permalink] New post   21 Jan 2021, 08:45
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In a barrack of soldiers there was stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack. For how many days shall the left over food last for the remaining soldiers?

(A) 175
(B) 200
(C) 225
(D) 250
(E) 270
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B
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Re: In a barrack of soldiers there was stock of food for 190 days for 4000 [#permalink] New post   22 Jan 2021, 09:28
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Initial food = (190 * 4000) man days

After 30 days the remaining food is there for 160 * 4000 Man days

Since 800 troops leave, the food will last for a different number of days. Let this = x

Remaining Man days = (4000 - 800) * x = 3200x

Therefore 160 * 4000 = 3200x

x = 200 days


Option B

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Re: In a barrack of soldiers there was stock of food for 190 days for 4000 [#permalink] New post   22 Jan 2021, 10:24
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Given: In a barrack of soldiers there was stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack.
Asked: For how many days shall the left over food last for the remaining soldiers?

Total stock of food = 190*4000 soldier-days
After 30 days stock of food left = 160*4000 soldier-days
Left over food will last for = 160*4000/(4000-800) = 160*4000/3200 = 200 days

IMO B
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Re: In a barrack of soldiers there was stock of food for 190 days for 4000 [#permalink] New post   26 Jan 2021, 05:55
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Bunuel wrote:
In a barrack of soldiers there was stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack. For how many days shall the left over food last for the remaining soldiers?

(A) 175
(B) 200
(C) 225
(D) 250
(E) 270

Solution:

We can let the stock of food be 190 x 4000 = 760,000 cheeseburgers. In other words, each soldier can have 1 cheeseburger per day. Since 30/190 = 3/19, then after 30 days, only 16/19 of the cheeseburgers are left and they have to feed 4000 - 800 = 3200 soldiers; therefore, they can last:

(16/19 x 760,000) / 3200 = 640,000/3200 = 200 days.

Answer: B
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Re: In a barrack of soldiers there was stock of food for 190 days for 4000 [#permalink] New post   02 Feb 2021, 13:44
Kinshook wrote:
Given: In a barrack of soldiers there was stock of food for 190 days for 4000 soldiers. After 30 days 800 soldiers left the barrack.
Asked: For how many days shall the left over food last for the remaining soldiers?

Total stock of food = 190*4000 soldier-days
After 30 days stock of food left = 160*4000 soldier-days
Left over food will last for = 160*4000/(4000-800) = 160*4000/3200 = 200 days

IMO B


the most precise & easy explanation for me. Thanks
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Re: In a barrack of soldiers there was stock of food for 190 days for 4000 [#permalink] New post   23 Feb 2022, 14:30
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Re: In a barrack of soldiers there was stock of food for 190 days for 4000 [#permalink]
23 Feb 2022, 14:30
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