Discussion
Rate of consumption of coal by a locomotive varies as the square of the speed and is 1000 kg/hour when the speed is 60 km/hour. If the coal costs the railway company 15 paise/kg and if the other expenses are 12 rupees/hour, what becomes the total cost with a speed of 30 km/hour ?
Answer: B
The total cost is 165 paise/km.
Coal use varies as the square of the speed, so halving the speed to 30 km/hour cuts it to a quarter:
\[ \begin{aligned} \text{coal} &= 1000 \times (30/60)^2 = 250 \text{ kg/h} \\ \text{coal cost} &= 250 \times 15 = 3750 \text{ paise/h} \\ \text{total} &= 3750 + 1200 = 4950 \text{ paise/h} \end{aligned} \]
\[ \text{per km} = 4950 / 30 = 165 \text{ paise/km} \]
49·5 is the hourly cost in rupees, not a cost per kilometre. 270 paise/km is the cost at the original 60 km/hour: (15000 + 1200) / 60. 'None of the above' is wrong because 165 is offered.
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