Latest CTS Aptitude Question SOLUTION: A clock hangs on the wall of a railway station, 71 ft. 9 in. long and 10 ft. 4 in. high. Those are the dimensions of the wall, not of the clock! While waiting for a train we notice

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A clock hangs on the wall of a railway station, 71 ft. 9 in. long and 10 ft. 4 in. high. Those are the dimensions of the wall, not of the clock! While waiting for a train we noticed that the hands of the clock were pointing in opposite directions, and were parallel to one of the diagonals of the wall. What was the exact time?

Asked In CTS Vignesh (12 years ago)

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Read Solution (2) :

shwe  (10 years ago)

Let us determine a diagonal of the wall

10 ft 4 inches = 124 inches
and
71 ft 9 inches = 861 inches

the tangent of the angle between the
bottom and top and a diagonal is

124/861

the inverse tangent of this is 8.1953°

thus the hour hand would have to be
at an angle of 81. 80469° to the
right of 12 o' clock high if the time is
ANY where between 12 and 3 in order
for this premise to be true.

At 3:00 it is at 90° and at 12:00 it is at zero.

The hour hand reaches this parallel position at

81.80469357
▬▬▬▬▬▬ X 3 hours
...90

which is

2.726823119 hours after 12

or

43.60938714 minutes after 2:00

or 2:43:36

I just verified that the minute hand would be at an angle of

261.6563228° at that time which is
81.65° away from the 6:00 position so it would, appear directly
opposite and within that minute, should be directly opposite the hour
hand.

Although that could round to 2:44, the exact time HAS not reached 2:44 yet
during the 2:43 minute. Therefore, the answer has to be

d which is 2:43

Is this solution Helpfull? Yes (5) | No (3)  

SIVASANGEETHA  (10 years ago)

there are four possiblities
11:25
5:55
7:35
1:35

Is this solution Helpfull? Yes | No (1)  

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