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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:

  1. $59 \frac{7}{12}\;\text{min. past 3}$
  2. $4 \;\text{p.m.}$
  3. $58 \frac{7}{11}\;\text{min. past 3}$
  4. $2 \frac{3}{11}\;\text{min. past 4}$

 

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.
59 7 min. past 3
12
B. 4 p.m.
C.
58 7 min. past 3
11
D.
2 3 min. past 4
11 
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3 min of right clock = (3+112)=3712 min of wrong clock

3/60 hr of right = 37/(12*60) hr of wrong

and wrong clock run 9hr 15 min from 7am to 4:15pm

so (9 + 15/60) = 37/4 hr of wrong = (3/60) * 3 * 60 = 9hr of right clock.

So right clock show 7am + 9hr = 4pm
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3 min of right clock = $(3 + \frac{1}{12}) = \frac{37}{12}$ min of wrong clock

3/60 hr of right = 37/(12*60) hr of wrong

and wrong clock run 9hr 15 min from 7am to 4:15pm

so (9 + 15/60) = 37/4 hr of wrong = (3/60) * 3 * 60 = 9hr of right clock.

So right clock show 7am + 9hr = 4pm
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