Multiple choice

Directions: The following question is accompanied by statements 1 and 2. You have to determine which of the following statements(s) is/are sufficient/necessary to answer the question. A car and a motorcycle start simultaneously from points P and Q, respectively, and travel towards each other. The distance between P and Q is 520 kilometres. Find the time taken by motorcycle to reach point P. Statement 1: The speeds of the car and the motorcycle are in the ratio 5 : 3. Statement 2: The car and the motorcycle meet each other after 5 hours.

  1. Statement 1 alone is sufficient.

  2. Statement 2 alone is sufficient.

  3. Both statements together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements 1 and 2 together are not sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be 5v and 3v. Total distance = 520. Time = 5 hours. 5v*5 + 3v*5 = 520 => 40v = 520 => v = 13. Speed of motorcycle = 3*13 = 39 km/h. Time to reach P = 520 / 39. Both statements are required to find the speed and the time.

AI explanation

Let the speeds of the car and motorcycle be 5x and 3x respectively, as given by the ratio in the first statement. Statement 1 alone only provides the ratio of their speeds, meaning the actual speeds remain unknown, so the time cannot be determined. Statement 2 alone states they meet after 5 hours, but without knowing their combined speed, you cannot find their individual speeds or the motorcycle's total time. Combining both statements, their combined speed is 520 km divided by 5 hours, which equals 104 km/hr; applying the ratio of 5 to 3 gives the motorcycle a speed of 39 km/hr, and the total time of 520 divided by 39 can then be calculated. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

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