Multiple choice

Directions: The following problem contains a question and three statements giving certain information. You have to read the statements carefully and decide which of the given statements is/are required to answer the question. Raj goes to school and comes back by the same route daily. His average speed is 5 km/hr for the to and fro journey. What is the time taken by him for the entire journey? I. Raj takes 30 minutes from home to school. II. Raj goes at 4 km/hr from school to home. III. Raj takes 25% more time when he comes from school to home than he takes when going from home to school.

  1. Only I

  2. Either II or III

  3. I and either II or III

  4. Only II

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = 2 * v1 * v2 / (v1 + v2). Given average speed = 5, we have 5 = 2 * v1 * v2 / (v1 + v2). Statement I gives time for one leg, which helps find distance. Statement II gives speed for return. Statement III gives time ratio. Combining I with either II or III allows calculating the full journey time.

AI explanation

The average speed for a to and fro journey is 2xy/(x+y), where x and y are the speeds for the two legs of the trip. Statement I provides the time for the first leg, and statement II provides the speed for the second leg, allowing you to find the second leg's time and calculate the total time. Statement III provides a relationship between the times of the two legs, which can be used with statement I to find the total time. Therefore, you need statement I along with either statement II or statement III to find the total time taken.

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