Multiple choice

Directions: The following problem consists of a question followed by two statements. Read the statements carefully and decide which of them is/are sufficient/necessary to answer the question. A man walks from his house at a speed of 9 km/hr and reaches his office 10 minutes late. Find the distance of the office from his house. I. If his speed had been 12 km/hr, he would have reached 20 minutes early. II. He walked in south direction and a man crossed him walking at a speed of 6 km/hr.

  1. Only statement II is sufficient.

  2. Both statements are necessary.

  3. Only statement I is sufficient.

  4. Neither statement I nor statement II is sufficient.

  5. Either statement I or statement II is sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let d be distance, t be time. d/9 = t + 1/6 (10 mins late). d/12 = t - 1/3 (20 mins early). Subtracting: d/9 - d/12 = 1/6 + 1/3 = 1/2. d/36 = 1/2, d = 18 km. Statement I is sufficient. Statement II is irrelevant.

AI explanation

Let the correct time to reach the office be t minutes. Using statement I, the difference in time taken at 9 km/hr and 12 km/hr to cover the distance d is 30 minutes (10 minutes late minus 20 minutes early), so d/9 - d/12 = 30/60. Solving this equation yields d/36 = 0.5, which gives the distance d as 18 km. Therefore, only statement I is sufficient to answer the question.

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