Multiple choice

Directions: The problem consists of a question and three statements numbered I, II and III given below it. You have to decide which of the given statements is/are sufficient to answer the question. Read all the statements and give answer accordingly. How far is the home from school? I. A started from home and B started from school simultaneously, with their speeds in the ratio of 4 : 5. II. B reached home 30 min earlier than A reached school. III. The difference between speeds of A and B is 8 kmph.

  1. I and III only

  2. II and III only

  3. I and II only

  4. All I, II and III together

  5. Data insufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D. Speed ratio A:B = 4:5. Let speeds be 4k and 5k. Time A = D/4k, Time B = D/5k. II says D/4k - D/5k = 30 min = 0.5 hr. D/20k = 0.5, so D = 10k. We need k to find D. III gives difference in speeds: 5k - 4k = 8, so k = 8. Thus D = 10 * 8 = 80 km. All three statements are required.

AI explanation

To find the distance between the home and school, you need the speeds of A and B and the time difference of their travel. Statement I gives the speed ratio of 4:5, statement III provides the actual speed difference of 8 kmph to find the exact speeds (32 kmph and 40 kmph), and statement II gives the 30-minute time difference to set up the equation. Using all three statements, you can calculate the exact time each person takes and multiply by their respective speeds to find the distance.

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