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A garrison has sufficient food for 75 soldiers for a period of 90 days

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Senior Manager
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A garrison has sufficient food for 75 soldiers for a period of 90 days  [#permalink]

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New post 15 Jan 2019, 13:39
10
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

53% (02:34) correct 47% (02:23) wrong based on 35 sessions

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A garrison has sufficient food for 75 soldiers for a period of 90 days. After 10 days, one-third of the soldiers leave. After another 10 days, 5 soldiers return. From this day on, how many days will the food last?

A.90
B.100
C.110
D.120
E.130
Intern
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Re: A garrison has sufficient food for 75 soldiers for a period of 90 days  [#permalink]

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New post 15 Jan 2019, 18:45
This one caught me for a while.

Where F represents food at the end of each period F0, F1, F2, F3

F0 = 75 * 90 = 6750

F1 = F0 - (75 soldiers * 10 days) = 6750 - 750 = 6000

F2 = F1 - (50 soldiers * 10 days) = 6000 - 500 = 5500

F3 = F2 - (55 soldiers * x days remaining), but F3 = 0 (no food left!)
0 = 5500 - 55x
x = 100 days remaining
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Re: A garrison has sufficient food for 75 soldiers for a period of 90 days  [#permalink]

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New post 15 Jan 2019, 22:06
total food =15*90
which should b equal to 75*10 + 50*10+ 100+55*x where x is the number of remainingdays

15*90 = 75*10 + 50*10+ 100+55*x
solving this equation of x gives me 100
hence B 100
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Re: A garrison has sufficient food for 75 soldiers for a period of 90 days   [#permalink] 15 Jan 2019, 22:06
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A garrison has sufficient food for 75 soldiers for a period of 90 days

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