Multiple choice

A bus takes $5$ hours more than a train to cover the distance of $900\ km$ from Vardha to Pune. If speed of the train is $15\ km/hr$ more than that of the bus, then what is the speed of bus per hour?

  1. $60\ km$
  2. $75\ km$
  3. $55\ km$
  4. $45\ km$
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D Correct answer
Explanation

Let speed of bus be v. Speed of train = v + 15. Time = distance / speed. 900/v - 900/(v+15) = 5. Dividing by 5: 180/v - 180/(v+15) = 1. 180(v+15-v) = v(v+15). 2700 = v^2 + 15v. v^2 + 15v - 2700 = 0. (v+60)(v-45) = 0. v = 45.

AI explanation

Let the speed of the bus be x km/hr, making the train's speed (x + 15) km/hr. Using the time equation 900/x - 900/(x + 15) = 5 and simplifying, we get x^2 + 15x - 2700 = 0. Factoring this quadratic equation results in (x + 60)(x - 45) = 0. Since speed must be positive, the speed of the bus is 45 km/hr.

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