Question:

Two buses start from opposite points of a main road, 150 km apart. The first bus runs for 25 km, takes a right turn and runs 15 km, then turns left and runs another 25 km, then takes a direction back to the main road. The other bus runs only 35 km along the main road. What is the distance between the two buses now?

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Draw a diagram and use Pythagoras theorem for perpendicular deviations from a straight path.
Updated On: Aug 11, 2025
  • 65 km
  • 75 km
  • 80 km
  • 85 km
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The Correct Option is A

Solution and Explanation

Initial distance = 150 km. First bus path: 25 km along main road ⇒ remaining distance along road = 125 km. Then 15 km perpendicular ⇒ displacement forms right triangle later. Then 25 km parallel to main road ⇒ horizontal shift increases by 25 km. Horizontal displacement of first bus from start = $25 + 25 = 50$ km, vertical displacement = 15 km. Second bus: 35 km along main road from other end ⇒ remaining road distance between vertical projections = $150 - 50 - 35 = 65$ km. Since vertical displacement = 15 km for first bus and 0 for second bus, actual distance = $\sqrt{65^2 + 15^2} = \sqrt{4225 + 225} = \sqrt{4450} \approx 66.8$ km. Closest option = 65 km.
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