BITSAT 2014 Paper

Let the speed of the train be v and distance to be covered be s so that total time taken is s/v hours. Cost of fuel per hour = kv2 (k is constant) Also 48 = k. 162 by given condition
∴ k =

3

16

∴ Cost to fuel per hour

3

16

v2
Other charges per hour are 300.
Total running cost
C= (

3

16

v62+300)

s

v

=

3s

16

v+

300s

v

dC

dv

=

3s

16

−

300s

v2

= 0 ⇒ v = 40

d2C

dv2

=

600s

v3

> 0
∴ v = 40 results in minimum running cost