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    A person has to cover a distance of 8km in 1 hour. If he covers one-fourth of the distance in one-third of the total time, then what should his speed
    Question

    A person has to cover a distance of 8km in 1 hour. If he covers one-fourth of the distance in one-third of the total time, then what should his speed (in km/h ) be to cover the remaining distance in the remaining time so that the person reaches the destination exactly on time?

    A.

    6

    B.

    7

    C.

    8

    D.

    9

    Correct option is D

    ​Given:

    Total distance = 8 km
    Total time = 1 hour

    Formula Used:

    Speed=DistanceTime \text{Speed} = \frac{\text{Distance}}{\text{Time}} ​​

    Solution:

    Distance covered in one-third of the time: 14×8=2 km Time taken for this part: 13×1=13 hour Remaining distance and time: Remaining distance=82=6 km Remaining time=113=23 hour Required speed: Speed=Remaining distanceRemaining time=623=6×32=9 km/h \text{Distance covered in one-third of the time:}\\ \ \\ \frac{1}{4} \times 8 = 2 \, \text{km} \\\ \\\text{Time taken for this part:} \\\ \\\frac{1}{3} \times 1 = \frac{1}{3} \, \text{hour} \\\ \\\text{Remaining distance and time:} \\\ \\\text{Remaining distance} = 8 - 2 = 6 \, \text{km} \\\ \\\text{Remaining time} = 1 - \frac{1}{3} = \frac{2}{3} \, \text{hour} \\\ \\\text{Required speed:} \\\ \\\text{Speed} = \frac{\text{Remaining distance}}{\text{Remaining time}} = \frac{6}{\frac{2}{3}} = 6 \times \frac{3}{2} = 9 \, \text{km/h} \\\ \\​​

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