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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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