A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time?
The correct answer is (A) 5:36 p.m..
Explanation:
The clock gains 10 minutes in every 24 hours. The clock was set right at 8:00 a.m. on Monday. We need to find the correct time when the clock shows 6:00 p.m. on Wednesday. Let us calculate the total time elapsed according to the faulty clock from Monday 8:00 a.m. to Wednesday 6:00 p.m.: From Monday 8:00 a.m. to Tuesday 8:00 a.m. is 24 hours. From Tuesday 8:00 a.m. to Wednesday 8:00 a.m. is another 24 hours. From Wednesday 8:00 a.m. to Wednesday 6:00 p.m. is 10 hours. Total time elapsed on the faulty clock = 24 + 24 + 10 = 58 hours. Since the clock gains 10 minutes in 24 hours, in 1 hours it gains 10/24 minutes. In 58 hours, the total time gained = 58 * (10 / 24) = 580 / 24 = 145 / 6 minutes = 24.166 minutes = 24 minutes and 10 seconds? Wait, let's calculate properly: The clock runs fast, so 24 hours 10 minutes of faulty clock time = 24 hours of actual time. That is, 145/6 hours of faulty clock time = 24 hours of actual time. Total faulty hours = 58 hours. Actual time elapsed = 58 * (24 / (145/6))? Wait: (24 hours of actual time) / (145/6 hours of clock time) * 58 = (24 * 6 / 145) * 58 = (144 / 145) * 58 = 144 * (2 / 5) = 288 / 5 = 57.6 hours of actual time. Let's convert 57.6 hours into hours and minutes: 57 hours + 0.6 * 60 minutes = 57 hours and 36 minutes. Now, add 57 hours and 36 minutes to Monday 8:00 a.m.: 57 hours = 48 hours (2 days, reaching Wednesday 8:00 a.m.) + 9 hours (reaching Wednesday 5:00 p.m.) + 36 minutes = Wednesday 5:36 p.m. Therefore, the correct time is 5:36 p.m.
हिंदी में प्रश्न एवं आदर्श उत्तर
कोई दीवार-घड़ी प्रत्येक 24 घंटे में 10 मिनट तेज चलती है । इस घड़ी को सोमवार को पूर्वाह्न 8:00 बजे सही समय दिखाने के लिए सही किया गया । जब यह घड़ी बुधवार को अपराह्न 6:00 बजे का समय दिखाती है, तो सही समय क्या है?
सही उत्तर (A) 5:36 p.m. है।
व्याख्या:
The clock gains 10 minutes in every 24 hours. The clock was set right at 8:00 a.m. on Monday. We need to find the correct time when the clock shows 6:00 p.m. on Wednesday. Let us calculate the total time elapsed according to the faulty clock from Monday 8:00 a.m. to Wednesday 6:00 p.m.: From Monday 8:00 a.m. to Tuesday 8:00 a.m. is 24 hours. From Tuesday 8:00 a.m. to Wednesday 8:00 a.m. is another 24 hours. From Wednesday 8:00 a.m. to Wednesday 6:00 p.m. is 10 hours. Total time elapsed on the faulty clock = 24 + 24 + 10 = 58 hours. Since the clock gains 10 minutes in 24 hours, in 1 hours it gains 10/24 minutes. In 58 hours, the total time gained = 58 * (10 / 24) = 580 / 24 = 145 / 6 minutes = 24.166 minutes = 24 minutes and 10 seconds? Wait, let's calculate properly: The clock runs fast, so 24 hours 10 minutes of faulty clock time = 24 hours of actual time. That is, 145/6 hours of faulty clock time = 24 hours of actual time. Total faulty hours = 58 hours. Actual time elapsed = 58 * (24 / (145/6))? Wait: (24 hours of actual time) / (145/6 hours of clock time) * 58 = (24 * 6 / 145) * 58 = (144 / 145) * 58 = 144 * (2 / 5) = 288 / 5 = 57.6 hours of actual time. Let's convert 57.6 hours into hours and minutes: 57 hours + 0.6 * 60 minutes = 57 hours and 36 minutes. Now, add 57 hours and 36 minutes to Monday 8:00 a.m.: 57 hours = 48 hours (2 days, reaching Wednesday 8:00 a.m.) + 9 hours (reaching Wednesday 5:00 p.m.) + 36 minutes = Wednesday 5:36 p.m. Therefore, the correct time is 5:36 p.m.