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    Question

    The speed of a car is 40% less than the speed

    of a bike. The time taken by a bus to cover (d-100) km distance in 9 hours. The sum of the speed of the bus and car is equal to the speed of the bike. If the time taken by car to cover (d+80) km distance is 2 hours more than the time taken by bike to cover (d+260) km distance, then which of the following statements is/are true? (i) The value of ‘d’ is the multiple of 16. (ii) The speed of the bike is 180 km/h. (iii) The time taken by the car to cover (d+80) km is 8 hours.
    A Only (i) and (iii) Correct Answer Incorrect Answer
    B Only (i) and (ii) Correct Answer Incorrect Answer
    C Only (ii) and (iii) Correct Answer Incorrect Answer
    D All (i), (ii) and (iii) Correct Answer Incorrect Answer
    E None of the given statements are true Correct Answer Incorrect Answer

    Solution

    The speed of a car is 40% less than the speed of a bike.

    Let’s assume the speed of a bike is ‘15y’.

    speed of a car = 15y of (100-40)%

    = 15y of 60%

    = 9y

    The sum of the speed of the bus and car is equal to the speed of the bike.

    speed of the bus = 15y-9y = 6y

    The time taken by a bus to cover (d-100) km distance in 9 hours.

    (d-100)/6y = 9

    (d-100) = 54y

    d = (54y+100)    Eq.(i)

    If the time taken by car to cover (d+80) km distance is 2 hours more than the time taken by bike to cover (d+260) km distance.

    (d+80)/9y = 2+ (d+260)/15y

    Put the value of ‘d’ from Eq.(i) in the above equation.

    (54y+100+80)/9y = 2+ (54y+100+260)/15y

    (54y+180)/9y = 2+ (54y+360)/15y

    (54y+180)/9y - (54y+360)/15y = 2

    After solving the above equation, 0.4y+20 = 24

    0.4y = 24-20

    0.4y = 4

    y = 10

    Put the value of ‘y’ in Eq.(i).

    d = (54x10+100) = 540+100 = 640

    (i) The value of ‘d’ is the multiple of 16.

    The above given statement is true.

    (ii) The speed of the bike is 180 km/h.

    Speed of bike = 15y = 15x10 = 150 km/h

    The above given statement is not true.

    (iii) The time taken by the car to cover (d+80) km is 8 hours.

    time taken by the car to cover (d+80) km = (d+80)/9y

    = (640+80)/(9x10)

    = 720/90

    = 8

    The above given statement is true.

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