Question

The fuel charges for running a train are proportional to the square of the speed generated in miles per hour and costs Rs. 48 per hour at 16 miles per hour. The most economical speed if the fixed charges i.e., salaries etc. amount to Rs. 300 per hour –

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

Answer: (C)

30

Answer 2

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 of fuel per hour (3/16) v²

Other charges per hour are 300.