A vehicle with mileage 15 km per litre contains 2 L of fuel. The vehicle gets some defect as a result of which 0.5 L of fuel gets wasted per hour when the engine is on. With what minimum speed the vehicle has to move to travel 20 km with the existing amount of fuel, if it travels with a uniform speed ?
[amp_mcq option1=”100 km per hour” option2=”120 km per hour” option3=”150 km per hour” option4=”200 km per hour” correct=”option1″]
This question was previously asked in
UPSC CAPF – 2016
The time taken for the journey is T = Distance / Speed = 20/S hours.
The fuel consumed for the travel based on mileage is (Distance / Mileage) = 20 km / (15 km/L) = 20/15 L = 4/3 L.
The defect causes fuel wastage at a rate of 0.5 L per hour while the engine is on.
Total fuel wasted = (Wastage rate per hour) * Time = 0.5 * T = 0.5 * (20/S) = 10/S L.
Total fuel consumed for the journey = Fuel for travel + Fuel wasted = 4/3 + 10/S.
The available fuel is 2 L. To complete the journey, the total fuel consumed must be less than or equal to the available fuel:
4/3 + 10/S <= 2 10/S <= 2 - 4/3 10/S <= (6 - 4)/3 10/S <= 2/3 To find the minimum speed S, we rearrange the inequality: S/10 >= 3/2
S >= 10 * (3/2)
S >= 15 km/hour.
The minimum speed required is 15 km/hour. All options (100, 120, 150, 200 km/hour) are greater than 15 km/hour and thus represent speeds at which the journey is possible. Among the given options, the minimum sufficient speed is 100 km per hour.