Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. What is the speed of the lorry? I. A man driving his car at the speed of 50 kmph observes that a lorry, travelling in opposite direction, takes 100 seconds to pass him. II. The lorry crosses a pole in 8 seconds and a 260-m long bridge in 10 seconds.

  1. The question can be answered by using statement I alone but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using any of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives relative speed (Lorry speed + 50 kmph) = Length / 100s. We don't know the length of the lorry, so we cannot find the speed. Statement II: Lorry crosses a pole in 8s (L = 8v) and a 260m bridge in 10s (L + 260 = 10v). Substituting L gives 8v + 260 = 10v, so 2v = 260, v = 130 m/s. Statement II is sufficient.

AI explanation

Using statement II, let the length of the lorry be L and its speed be S; crossing a pole gives S equals L divided by 8, and crossing the 260-meter bridge gives S equals (L + 260) divided by 10. Equating the two expressions, L/8 = (L + 260)/10, which solves to L = 1040 meters and S = 130 m/s, making statement II alone sufficient. Statement I lacks the length of the lorry, so a crossing time of 100 seconds cannot determine its individual speed. Therefore, the question can be answered by using statement II alone but cannot be answered by using statement I alone.

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