Directions : Read the following passage carefully and answer the questions…
2022
Directions : Read the following passage carefully and answer the questions given below.
Three people A, B & C started their journey at 9:30 am, 11:30 am & 2 pm respectively from point X to Y. B reached the destination at 7:30 pm of the same day. B is fastest and C is not the slowest.
Which of the following statement/s is/are correct?
(A) C reached the destination in 6 hours and A reached the destination in 4.5 hours.
(B) C reached the destination in 5 hours and A reached the destination in 9 hours.
(C) If distance increased by 180 km and speed of C is 1/6th of the speed of B, then A reached the new destination at 4:20 pm.
- A.
Both (B) & (C)
- B.
None of these
- C.
Both (A) & (B)
- D.
Only (B)
- E.
Only (A)
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
For two travellers covering the same distance, speed and time are inversely related - the traveller who takes less time is the faster one. So if B is stated to be the fastest of A, B and C, then B's own travel time must be the smallest of the three - no other traveller's time can be shorter than B's.
Working it out
B started at 11:30 am and reached the destination at 7:30 pm, so B's own travel time works out to 8 hours.
Since B is the fastest, no other traveller's time can be shorter than B's 8 hours - in particular, C's actual travel time must be more than 8 hours.
Statement (A) states C's time as 6 hours - that is less than B's 8 hours, which would make C faster than B. This directly breaks the 'B is fastest' condition, so statement (A) cannot be accepted.
Statement (B) states C's time as 5 hours - again less than B's 8 hours, breaking the same condition. So statement (B) cannot be accepted either.
Both offered statements fail on the same ground (C's stated time undercuts B's actual 8-hour time), regardless of what either statement says about A's time.
Cross-check
Every option other than 'None of these' needs statement (A) and/or statement (B) to hold - there is no option built on statement (C) alone. Since both (A) and (B) are ruled out, every one of those options fails together, leaving only the option that says neither statement is correct.
Note on statement (C): the only option that pairs statement (C) with anything is the one naming statement (B) alongside it, and that pairing already needs statement (B) to hold. Since statement (B) fails the check above, that option is ruled out without needing to separately verify statement (C)'s own claim about the new distance and A's new arrival time.