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    A bus travelling with 57\frac5775​​ of its actual speed covers 42 km in 1 h 40 min 48 s. Find the actual speed of the bus.
    Question

    A bus travelling with 57\frac57​ of its actual speed covers 42 km in 1 h 40 min 48 s. Find the actual speed of the bus.

    A.

    30 km/h

    B.

    35 km/h

    C.

    1767\frac67​km/h

    D.

    25 km/h

    Correct option is B

    Given:

    Time taken=1 hr 40 min 48 sec=1 hr+4060 hr+483600 hr=12675 hrDistance travelled=42 km\text{Time taken} = 1 \, hr \, 40 \, min \, 48 \, sec = 1 \, hr + \frac{40}{60} \, hr + \frac{48}{3600} \, hr = \frac{126}{75} \, hr \\\text{Distance travelled} = 42 \, km \\​​

    Formula Used:

    Speed=distancetime\text{Speed} = \frac{\text{distance}}{\text{time}} ​​

    Solution:

    Time taken=1 hr 40 min 48 sec=1 hr+4060 hr+483600 hr=12675 hrDistance travelled=42 kmSpeed=distancetime=4212675=42×75126Speed of car=(57)×actual speed=>Actual speed=42×75126×75=7×5=35 km/hr\text{Time taken} = 1 \, hr \, 40 \, min \, 48 \, sec = 1 \, hr + \frac{40}{60} \, hr + \frac{48}{3600} \, hr = \frac{126}{75} \, hr \\\text{Distance travelled} = 42 \, km \\\text{Speed} = \frac{\text{distance}}{\text{time}} = \frac{42}{\frac{126}{75}} = \frac{42 \times 75}{126} \\\therefore \text{Speed of car} = \left(\frac{5}{7}\right) \times \text{actual speed} \\\Rightarrow \text{Actual speed} = \frac{42 \times 75}{126} \times \frac{7}{5} = 7 \times 5 = 35 \, km/hr​​

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