Directions: Read the following passage carefully and answer the question given…
2022
Directions: Read the following passage carefully and answer the question given below.
Three people A, B and C started their journey from point X to point Y at 9:30 am, 11:30 am and 2:00 pm respectively. B is the fastest and C is not the slowest. B reached the destination at 7:30 pm on the same day.
If the speed of A is 25% less than the speed of B, then which of the following statement(s) is/are correct about A's journey?
(A) A takes 2 hours 40 minutes more than B to reach the destination.
(B) A reaches the destination at 8:10 pm.
(C) The total time taken by A and B together to reach the destination is 19 hours 40 minutes.
- A.
Both (A) & (B)
- B.
Only (B)
- C.
Both (B) & (C)
- D.
Only (C)
- E.
Both (A) & (C)
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
When two bodies cover the same distance, time is inversely proportional to speed: T = D / S, so for a fixed D, T is proportional to 1/S. If one speed is a fraction k of another, that body's time is 1/k of the other's time for the same route.
Application
B's travel time: B starts at 11:30 am and arrives at 7:30 pm, so B takes 8 hours for distance XY.
A's speed is 25% less than B's, so A's speed = 0.75 times (B's speed). For the same distance XY, A's time = B's time divided by 0.75 = 8 divided by 0.75 = 32/3 hours = 10 hours 40 minutes.
Statement (A): A's time minus B's time = 10 h 40 min minus 8 h = 2 hours 40 minutes more than B. So (A) is correct.
Statement (B): A starts at 9:30 am and takes 10 h 40 min, so A arrives at 9:30 am + 10 h 40 min = 8:10 pm. So (B) is correct.
Statement (C): Total time of A and B = 10 h 40 min + 8 h = 18 hours 40 minutes, not 19 hours 40 minutes. So (C) is incorrect.
Cross-check
A is the slowest (B fastest, C not slowest), which is consistent with A's speed being only 0.75 of B's. Statements (A) and (B) both hold while (C) is off by exactly one hour, so the choice naming statements (A) and (B) together is the one that matches.