On her way to the office, Neeta travels at a constant speed throughout. She…
2025
On her way to the office, Neeta travels at a constant speed throughout. She reaches a bus stand at 1/6th of the distance of her journey and a temple at 2/3rd of the distance of her journey. The time taken by her to travel between the temple and the bus stand is 15 minutes. She reaches the bus stand at 8:25 am. At what time did she start from her house, and at what time did she reach her office?
- A.
8:10 am and 8:45 am
- B.
8:15 am and 8:55 am
- C.
8:20 am and 8:50 am
- D.
8:15 am and 9:00 am
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept: When a journey is covered at a constant speed, the fraction of distance covered up to any point equals the fraction of total time taken to reach that point. So the time between any two markers on the journey equals (fraction of the journey between them) times (total journey time).
Neeta reaches the bus stand at 1/6 of the journey and the temple at 2/3 of the journey.
Fraction of the journey between the bus stand and the temple = 2/3 - 1/6 = 4/6 - 1/6 = 3/6 = 1/2.
This 1/2 of the journey takes 15 minutes, so the total journey time = 15 x 2 = 30 minutes.
Time to reach the bus stand = 1/6 of the total journey time = 1/6 x 30 = 5 minutes.
She reaches the bus stand at 8:25 am, so she started 5 minutes earlier: 8:25 am - 5 minutes = 8:20 am.
She reaches the office at start time + total journey time = 8:20 am + 30 minutes = 8:50 am.
Cross-check: From 8:20 am, the bus stand (1/6 of 30 minutes = 5 minutes) falls at 8:25 am, matching the given data. The temple (2/3 of 30 minutes = 20 minutes) falls at 8:40 am, so the bus-stand-to-temple gap is 8:40 am - 8:25 am = 15 minutes, matching the question. The temple-to-office gap is the remaining 1/3 of 30 minutes = 10 minutes, giving 8:40 am + 10 minutes = 8:50 am, consistent with the total. So Neeta started at 8:20 am and reached the office at 8:50 am.