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120 men had provision for 200 days. After 5 days , 30 men died due to an epidemic. The remaining food will last for ________?​

Sagot :

Let x = the amount of food per person per day.

Then, the total amount of food, n, is:

n = 120 × 200 × x

n = 24000x.

Now, after 5 days, the remaining food, f, is:

f = n-(5 × 120 × x)

= n – 600x

Plug in n = 24000x.

f = 24000x – 600x

f = 23400x.

Now, the amount of food per day, m, is:

m = (120 – 30) × x = 90x

Thus, the remaining food will last for.

[tex]\sf\large{ \frac{f}{m} = \frac{23400x}{90x}}[/tex]

= [tex]\sf\large{ \frac{260\:×\:\cancel{90x}}{\cancel{90x}}}[/tex]

= 260

Answer: 260 days