कोई व्यक्ति घर से 14:30 बजे निकला और यात्रा कर गाँव पहुँचा, तब गाँव की घड़ी ने 15:15 बजे का समय दिखाया। वहाँ 25 मिनट रुककर, वह पहले वाले मार्ग की अपेक्षा 1:25 गुना लम्बे मार्ग से, दोगुनी चाल से यात्रा कर 16:00 बजे अपने घर पहुँचा। घर की घड़ी की तुलना में गाँव की घड़ी
सही उत्तर (B) 5 minutes slow है।
व्याख्या:
Let us analyze the journey times according to home clock: Departure time from home = 14:30 hours. Arrival time at village according to village clock = 15:15 hours (Duration elapsed on village clock = 45 minutes). Stay at village = 25 minutes. Return journey started after 25 minutes. Return journey length = 1·25 times the first route. Speed on return = twice as fast (2 times). Therefore, return time = (Distance ratio 1·25) / (Speed ratio 2) = 1·25 / 2 = 0·625 times the outward travel time. If outward travel time was 45 minutes according to village clock, return travel time = 45 × 0·625 = 28·125 minutes? Wait, let's calculate using home clock: Total time elapsed from departure (14:30) to return (16:00) according to home clock = 1 hour 30 minutes = 90 minutes. Stay duration = 25 minutes. Total travel time (outward + return) according to home clock = 90 - 25 = 65 minutes. Let outward journey time be t. Return journey time = 1·25 / 2 t = 0·625 t. Total travel time = t + 0·625 t = 1·625 t = 65 minutes. Therefore, t = 65 / 1·625 = 40 minutes. Thus, the outward journey took 40 minutes according to the home clock. The village clock showed 45 minutes for the exact same outward journey (from 14:30 to 15:15 is 45 minutes). Comparing the two: home clock took 40 minutes, while village clock elapsed 45 minutes. This means the village clock is 5 minutes ahead (fast). Hence, option (d) is correct.
In English (Question & Model Answer)
A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1·25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is
The correct answer is (B) 5 minutes slow.
Explanation:
Let us analyze the journey times according to home clock: Departure time from home = 14:30 hours. Arrival time at village according to village clock = 15:15 hours (Duration elapsed on village clock = 45 minutes). Stay at village = 25 minutes. Return journey started after 25 minutes. Return journey length = 1·25 times the first route. Speed on return = twice as fast (2 times). Therefore, return time = (Distance ratio 1·25) / (Speed ratio 2) = 1·25 / 2 = 0·625 times the outward travel time. If outward travel time was 45 minutes according to village clock, return travel time = 45 × 0·625 = 28·125 minutes? Wait, let's calculate using home clock: Total time elapsed from departure (14:30) to return (16:00) according to home clock = 1 hour 30 minutes = 90 minutes. Stay duration = 25 minutes. Total travel time (outward + return) according to home clock = 90 - 25 = 65 minutes. Let outward journey time be t. Return journey time = 1·25 / 2 t = 0·625 t. Total travel time = t + 0·625 t = 1·625 t = 65 minutes. Therefore, t = 65 / 1·625 = 40 minutes. Thus, the outward journey took 40 minutes according to the home clock. The village clock showed 45 minutes for the exact same outward journey (from 14:30 to 15:15 is 45 minutes). Comparing the two: home clock took 40 minutes, while village clock elapsed 45 minutes. This means the village clock is 5 minutes ahead (fast). Hence, option (d) is correct.