Question

The cost of running a bus from A to B, is ₹`(av + b/v)`, where v km/h is the average speed of the bus. When the bus travels at 30 km/h, the cost comes out to be ₹ 75 while at 40 km/h, it is ₹ 65. Then the most economical speed (in km/h) of the bus is ______.

Options

• 45

• 50

• 60

• 40

Answer 1

The cost of running a bus from A to B, is ₹`(av + b/v)`, where v km/h is the average speed of the bus. When the bus travels at 30 km/h, the cost comes out to be ₹ 75 while at 40 km/h, it is ₹ 65. Then the most economical speed (in km/h) of the bus is 60.

Explanation:

Let cost C = `av + b/v`

According to given question,

`30a + b/30` = 75  ...(i)

`40a + b/40` = 65  ...(ii)

On solving (i) and (ii), we get a = `1/2` and b = 1800

Now, C = `av + b/v \implies (dC)/(dv) = a - b/v^2`

`(dC)/(dv) = 0 implies a - b/v^2 = 0 \implies v = sqrt(b/a) = sqrt(3600)`

`\implies` v = 60 kmph