Multiple choice

Two cities A and B are 90 km apart from each other. Mohan started from city A and Sohan started from city B at the same time. If both of them proceed in the same direction, they will meet in 9 hours and if they proceed in opposite directions, they will meet in 9/7 hours. Calculate their speeds (in km/hr).

  1. 10 km/hr and 30 km/hr

  2. 40 km/hr and 10 km/hr

  3. 40 km/hr and 30 km/hr

  4. 90 km/hr and 70 km/hr

  5. 10 km/hr and 90 km/hr
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be u and v. Relative speed in same direction is u - v = 90/9 = 10. Relative speed in opposite direction is u + v = 90/(9/7) = 70. Solving the system u - v = 10 and u + v = 70 gives u = 40 and v = 30.

AI explanation

Let the speeds of Mohan and Sohan be x km/hr and y km/hr. When moving in opposite directions, their relative speed is x + y, so 90 / (x + y) = 9/7, which simplifies to x + y = 70. When moving in the same direction, their relative speed is x - y, so 90 / (x - y) = 9, which simplifies to x - y = 10. Solving the equations x + y = 70 and x - y = 10 yields x = 40 and y = 30. The speeds are 40 km/hr and 30 km/hr.

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