In a fort there was sufficient food for $200$ soldiers for $31$ days. After $27$ days $120$ soldiers left the fort. For how many extra days will the rest of the food last for remaining soldiers ?

6

days

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8

days

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10

days

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12

days

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Solution

The correct option is A $10$ days
Give,
Total Soldiers = 200
Food for them = 31 days
So, Quantity of food = 200 31 = 6200 man-days
Till 27 days, quantity consumed = 27 200 = 5400 man-days
Rest quantity = 6200 - 5400 = 800 man-days
Remaining soldiers = 200 - 120 = 80
Let remaining food will sufficient for x days
Now,
5400 + 80 x = 6200
80 x = 800
x = 10 days

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