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A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 O'clock, the true time is -
  • a)
    4 p.m.
  • b)
    59(7/12) minutes past 3
  • c)
    58(7/11) minutes past 3
  • d)
    2(3/11) minutes past 4
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In...
(a) Time from 7 a.m. to quarter pas 4
= 9 hours 15 min.= 555 min.
Now, 37/12 min. of this watch = 3 min. of the correct watch
555 min. of this watch
of the correct watch.
Correct time is 9 hours after 7 a.m. i.e . 4 p m.
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Most Upvoted Answer
A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In...
Problem:
A watch gains 5 seconds in 3 minutes and was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, what is the true time?

Solution:
To solve this problem, we need to determine the time that has actually passed based on the time shown on the watch. Let's break down the problem into smaller steps.

Step 1: Determine the time elapsed from 7 a.m. to quarter past 4 o'clock:
The time elapsed from 7 a.m. to quarter past 4 o'clock is 9 hours and 15 minutes.
9 hours = 9 * 60 = 540 minutes
15 minutes = 15 minutes
Total time elapsed = 540 + 15 = 555 minutes.

Step 2: Calculate the time that the watch would have gained in 555 minutes:
The watch gains 5 seconds in 3 minutes.
So, in 1 minute, the watch gains 5/3 seconds.
In 555 minutes, the watch would have gained (5/3) * 555 seconds.

Step 3: Convert the gained time to minutes:
To convert the gained time from seconds to minutes, we need to divide it by 60.
So, the watch would have gained ((5/3) * 555) / 60 minutes.

Step 4: Subtract the gained time from the indicated time on the watch:
The watch indicates quarter past 4 o'clock, which is 4 hours and 15 minutes.
4 hours = 4 * 60 = 240 minutes
15 minutes = 15 minutes
Total indicated time = 240 + 15 = 255 minutes.

Subtracting the gained time ((5/3) * 555) / 60 from the indicated time 255, we get:
255 - ((5/3) * 555) / 60.

Step 5: Calculate the true time:
To calculate the true time, we need to subtract the gained time from the indicated time.
255 - ((5/3) * 555) / 60 = 240 - (925/3) / 60 = 240 - 15.42 = 224.58 minutes.

Converting 224.58 minutes to hours and minutes:
224.58 minutes = 3 hours and 44.58 minutes.

Therefore, the true time is approximately 3 hours and 44.58 minutes after 7 a.m., which is close to 4 p.m. (option A).
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A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 O'clock, the true time is -a)4 p.m.b)59(7/12) minutes past 3c)58(7/11) minutes past 3d)2(3/11) minutes past 4Correct answer is option 'A'. Can you explain this answer?
Question Description
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