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A garrison has sufficient food for 75 soldiers for a period of 90 days 28 Dec 2019, 01:42
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C
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55% (hard)

Question Stats:

70% (02:29) correct 30% (02:55) wrong based on 225 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. 80
B. 90
C. 100
D. 110
E. 120
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C
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A garrison has sufficient food for 75 soldiers for a period of 90 days 28 Dec 2019, 03:36
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Let us say each soldier eats 1 meal per day . You have 75∗90 meals.First 10 days you use 75∗10 meals. Second 10 days, you use 50∗10 meals. You now have M=75∗90−75∗10−50∗10 meals = 5500 meals. You now have 55 soldiers. Therefore, no. of days = M/55=100.
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A garrison has sufficient food for 75 soldiers for a period of 90 days 29 Dec 2019, 04:43
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Solution



Given
    • 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

To find
    • How many more days will the food last?

Approach and Working out
Food left after the first lot of soldiers left = 75 x 90 – 75 x 10 = 6000
Food left after the second lot of soldiers left = 6000 – (75 x 2/3) x 10 = 5500
    • The remaining days = 5500/(50 + 5) = 100 days

Thus, option C is the correct answer.

Correct Answer: Option C
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A garrison has sufficient food for 75 soldiers for a period of 90 days 28 Aug 2021, 08:00
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Solution:

We have sufficient food for 75 soldiers for a period of 90 days.

So we can infer we have \(75\times 90=6750\) units of food.

In \(10\) days, \(75\) soldiers must have consumed \(75\times 10 = 750\) units of food. So we are left with \(6750-750=6000\) units.

We are given that After \(10\) days, one-third which means \(\frac{2}{3}\times 75= 50\) soldiers left.

In next \(10\) days, \(50\) soldiers must have consumed \(50\times 10 = 500\) units of food. So we are left with \(6000-500=5500\) units.

\(5\) soldiers return and now we have \(55\) soldiers and \(5500\) units of food.

So, the number of days this food will last \(= \frac{5500}{55}=100\)

Hence the right answer is Option C.
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A garrison has sufficient food for 75 soldiers for a period of 90 days 28 Aug 2021, 10:52
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M1 D1 = 75 * 90

After 10 days, one-third of the soldiers or 25 soldiers leave and we are left with 75-25=50 soldiers.

The 75 soldiers worked for 10 days.

After another 10 days, 5 soldiers return, and so for these 10 days 50 soldiers worked and we have 55 soldiers working for x days now.

So 75 * 90 = (75 * 10) + (10*50) + (x * 55)

=>75 *90 = 1250 + 55x

=> 55x = 75 * 90 -1250

= 6750 -1250 = 5500

=>x = 100

(option c)

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A garrison has sufficient food for 75 soldiers for a period of 90 days 23 Jul 2024, 20:36
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