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olya-2409 [2.1K]
3 years ago
13

A garrison of 400men had food for 40days.After 10 days,200 more men joined them .How long will the food last now?(Assume that th

e food taken by each man is almost the same.​
Mathematics
1 answer:
mestny [16]3 years ago
6 0

Let x be the amount of food needed for one man for one day. At the beginning, we have enough food for 400 men for 40 days, i.e.

400\cdot 40\cdot x = 16000x

After 10 days, the 400 men will have consumed

400\cdot 10\cdot x = 4000x

food, impliying that the food remaining is

16000x-4000x=12000x

If 200 more men join the garrison, there are now 600 men. Each of them requires x food each day, and there are 12000x units of food remaining. They will last

\dfrac{12000x}{600}=20 days.

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4. So now we can do a similar thing with the first half of our equation and convert it into a fraction and not a mixed number.

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Now we multiply divide them, and the easiest way I learned how to do this was by keep the first fraction in its place, and flipping the denominator and numerator of the second, and multiplying them.

so   \frac{58}{21} * \frac{3}{10} which if we multiply both sides, you get \frac{174}{210}

I'll save you some times and simplify it for you, the greatest common factor is 6 so we divide the top and bottom by 6 to get

\frac{29}{35}

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