Question

A fort had provisions for 450 men for 80 days. After 10 days, 50 more men arrived. How long will the remaining food last at the same rate? (Direct and inverse variation)

Answer 1

Step-by-step explanation:

$no \: of \: men \: at \: the \: beginning = 450 \\ no \: of \: men \: arrived \: after \: 10 \: days \: = 50 \\ total \: no \: of \: men \: = 450 + 50 = 500 \\ after \: 10 \: days \: period = 70days \\ after \: 10 \: days \: there \: will \: be \: 500 \: men \\ so \: : \\ let \: x \: be \: the \: number \: of \: days \: till \: which \: the \: food \: remains \: \\ 450:500 = 70:x \\ by \: inverse \: propotion \\ 500:450 = 70:x \\ \frac{500}{450} = \frac{70}{x} \\ x = 70 \times \frac{450}{500} \\ x = 63$

So the food will remain for 63 days..

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