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# 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.

Jitender Singh IIT Delhi
6 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