Multiple choice

Directions: In the following problem, a question is followed by statements marked (I), (II) and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. To cover some distance, a man travelled at 40 kmph for some time and then at 50 kmph. For how much time did he travel in total? I. Total journey was of 250 km. II. He covered less than half of the journey at the speed of 40 kmph. III. He travelled 50 km more at the speed of 50 kmph than at the speed of 40 kmph.

  1. Only statements I and II

  2. Only statements I and III

  3. Only statements II and III

  4. All three statements together

  5. None of the statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let t1 be time at 40 kmph and t2 be time at 50 kmph. Total distance D = 40t1 + 50t2. Statement I: 40t1 + 50t2 = 250. Statement III: 50t2 = 40t1 + 50. Substituting III into I: 40t1 + (40t1 + 50) = 250 => 80t1 = 200 => t1 = 2.5. Then 50t2 = 100 + 50 = 150 => t2 = 3. Total time = 5.5. Both I and III are needed.

AI explanation

Let the man travel for t hours at 40 kmph, so he covers 40t km; for the remaining time T minus t, he travels at 50 kmph and covers 50(T minus t) km. From statement I, 40t plus 50(T minus t) equals 250, and from statement III, 50(T minus t) minus 40t equals 50; adding these two equations gives 100(T minus t) equals 300, so the time spent at 50 kmph is 3 hours. Subtracting this 50 km difference from the 250 km total journey shows that 200 km were covered at both speeds combined, which allows you to easily solve for the remaining time and find the total time T. Statement II only provides an inequality, making it unnecessary, so only statements I and III are sufficient.

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