Multiple choice

Two friends x and y started from city P and went to city Q, which was 240 km away. Mr. x maintained a speed of 40 kmph for a certain distance and then increased his speed to 60 kmph, whereas Mr. y started with 30 kmph and exactly at half the way through increased his speed to 80 kmph. If both x and y reached Q at the same time, then at what distance from P did Mr. x change his speed?

  1. 130 km

  2. 150 km

  3. 180 km

  4. 200 km

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total distance = 240 km. Y travels at 30 km/h for 120 km (4 hours) and 80 km/h for 120 km (1.5 hours). Total time = 5.5 hours. X travels d km at 40 km/h and (240-d) km at 60 km/h. d/40 + (240-d)/60 = 5.5. Multiply by 120: 3d + 2(240-d) = 660. 3d + 480 - 2d = 660. d = 180.

AI explanation

Mr. y covers the first 120 km at 30 kmph in 4 hours and the remaining 120 km at 80 kmph in 1.5 hours, for a total time of 5.5 hours. Let d be the distance Mr. x travels at 40 kmph before changing to 60 kmph for the remaining (240 - d) kilometers. Setting his total time to 5.5 hours gives (d / 40) + ((240 - d) / 60) = 5.5, and multiplying by 120 results in 3d + 480 - 2d = 660. Solving this equation gives d = 180, meaning Mr. x changed his speed at 180 km from P.

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