Question 24

The rate at which coal is consumed by a RORO train, which is operated by Konkan Railways,fluctuates as the square of the speed. It is given that coal consumption of this train is 1200 kg/hour whenthe speed is 40 km/hour. Konkan Railway bears the cost of coal at the rate Rs. 16/100kg and all otherexpenses of running the RORO train costs Konkan Railways Rs. 13/hour. Find the total cost in paise/km, foroperating the RORO train when it is running at the speed of V km/hour.

Solution

Let rate of consumption per hour be R

Therefore, $$R=k\left(V^2\right)$$

When speed= 40km/hr R= 1200kg/hr

So, When speed = V

R= $$\left(\frac{1200}{1600}\right)\times\ V^2$$

Cost of coal consumed per hour = $$\left(\frac{1200}{1600}\right)\times\ V^2\times\ \frac{16}{100}=\frac{12}{100}V^2$$

All other expenses = Rs 13/ hr

Therefore operating cost per hour = Rs.($$13+\frac{12}{100}V^2$$)

Operation cos in paise per hour = $$1300+12V^2$$

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