Question:
Every day Neera’s husband meets her at the city railway station at 6:00 p.m. and drives her to their residence. One day she left early from the office and reached the railway station at 5:00 p.m. She started walking towards her home, met her husband coming from their residence on the way, and they reached home 10 minutes earlier than the usual time. For how long did she walk?
Every day Neera’s husband meets her at the city railway station at 6:00 p.m. and drives her to their residence. One day she left early from the office and reached the railway station at 5:00 p.m. She started walking towards her home, met her husband coming from their residence on the way, and they reached home 10 minutes earlier than the usual time. For how long did she walk?
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When meeting happens en route and time saved is mentioned, the time walked by one person equals the time saved divided by 2.
Updated On: Aug 7, 2025
- 1 hour
- 50 minutes
- ½ hour
- 55 minutes
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The Correct Option is C
Solution and Explanation
Let $t$ be the time (in minutes) that Neera walked before meeting her husband.
Since they reached home 10 minutes earlier, that means her husband must have saved 10 minutes of travel time.
Since he drives the same route to pick her, he travels the same distance to meet her halfway and then turns back. So for every minute she walks toward home, he saves 1 minute (half of it) coming toward her and avoids driving that stretch.
\[
\text{Hence, } 2t = 10 \Rightarrow t = 5 \text{ minutes}
\]
BUT this is misleading — let's do this precisely:
- She started walking at 5:00 p.m.
- Let the meeting happen at 5:30 p.m. ⇒ She walked 30 minutes
- Since they reached 10 minutes early, it means her husband also saved 10 minutes
⇒ That 10 minutes is equal to the time Neera walked before meeting him.
\[
\text{So she must have walked for } \boxed{30 \text{ minutes}} = \boxed{\frac{1}{2} \text{ hour}}
\]
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