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Grade 12Differential Calculus

the cost of fuel for running a bus is proportional to the square of the speed generated in km/hr. it costs Rs.48 per hour when the bus is mooving at the speed of 20km/hr .what is the most economical speed if the fixed charges are Rs.108 for an hour,over and above the running charges.

Anu Maan

16 Years agoGrade 12

1 Answer

Jitender Singh

12 Years ago

Ans:

Let cost of fuel be ‘P’ Rs/hr & spped of vehicle be ‘v’ in km/hr.

$P \alpha v^{2}$

$P = av^{2}, a = constant$

$48 = a(20)^{2}$

$a = \frac{48}{20^{2}} = \frac{3}{25}$

$P = \frac{3}{25}v^{2}$

There is something missing in the question. How much distance bus need to cover should mention. Otherwise, at

$P = 108 (\frac{Rs.}{hr})$

$108 = \frac{3}{25}v^{2}$

$v = 30 (\frac{km}{hr})$

Thanks & Regards

Jitender Singh

IIT Delhi

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