Multiple choice

Anil travelled from place A to place B and after covering half the distance increased his speed by 50%. As a result, he covered the entire journey in 2 hours less time. What will be the total time taken by him if his speed is decreased by 50% in the second half?

  1. 14 hours

  2. 16 hours

  3. 18 hours

  4. 24 hours

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

Let total distance be 2D and initial speed be v. Time taken = D/v + D/v = 2D/v. New scenario: D/v + D/(1.5v) = 2D/v - 2. D/v * (1 + 2/3) = 2D/v - 2. (5/3) * (D/v) = 2D/v - 2. 2 = (1/3) * (D/v) => D/v = 6. Total time = 12 hours. If speed is decreased by 50% in the second half: D/v + D/(0.5v) = 6 + 12 = 18 hours.

AI explanation

Let the total distance be D and Anil's initial speed be S, making his normal total time D/S. When his speed increases by 50% for the second half, his new speed for that part is 1.5S, and the time equation becomes D/2S + D/3S = D/S - 2. Solving this gives the original total time as 12 hours, meaning the first half took 6 hours. If he decreases his speed by 50% for the second half, his new speed becomes 0.5S, so the second half will take 12 hours, making the total time 6 + 12 = 18 hours.

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