Multiple choice

Three cars started simultaneously from Ajmer to Benaras along the same highway. The second car travelled with a speed that was 10 km/h higher than the first car's speed and arrived at Benaras 1 hour earlier than the first car. The third car arrived at Benaras 33.33 minutes earlier than the first car, travelling half the time at the speed of the first car and the other half at the speed of the second car. Find the total distance covered by these three cars during their journeybetween Ajmer and Benaras.

  1. 360 km

  2. 600 km

  3. 540 km

  4. 840 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D and speed of first car be v. Second car speed = v+10. Time difference = 1 hour. D/v - D/(v+10) = 1. Third car speed = (v + v+10)/2 = v+5. Time difference = 33.33 min = 1/3 hour. D/v - D/(v+5) = 1/3. Solving these equations yields D = 600 km.

AI explanation

Let the speed of the first car be v km/h and the time taken be t hours, so the distance is v times t. The average speed of the third car is (v + v + 10)/2 = v + 5, and since its time is t - 1/2, we have v times t = (v + 5)(t - 1/2). From the second car's data, v times t = (v + 10)(t - 1), and solving these two equations gives v = 30 and t = 10. Therefore, the total distance covered by all three cars is 3 times v times t, which is 600 km.

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