CAT Questions Based Clock

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CAT Questions Based Clock:

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Question 1:

There is a clock which loses 5 minutes after every hour. It shows correct time at 9 o clock on Wednesday on 1st September. Among the following options, when will it show the correct time of 9 o clock again?

a) Friday,10th September
b) Tuesday,14th September
c) Monday, 13th September
d) Monday, 6th September

Question 2:

Ram has a digital watch that shows time in a 24 hour format. The time on the watch is 4:56. How many minutes will pass before the watch next shows a time with digits in an ascending order from left to right?

a) 71
b) 459
c) 457
d) 458

Question 3:

X, Y and Z ran a 50 m race. The time taken by X was recorded by watch W1 and the time taken by Y and Z was recorded by watch W2. The time taken by X, Y and Z to complete the race according to the respective watches used was 5, 6 and 3 seconds respectively. W2 is a faulty clock and loses time uniformly. If X beats Y by 10 m, what was the speed of Z during the race?

a) 26
b) 96
c) 16
d) 56

Question 4:

In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hr 18 min and 15s of normal time. What is the time gained or lost by this watch in one day?

a) 14 min 10 s lost
b) 13 min 48 s lost
c) 13 min 20 s gained
d) 14 min 40 s gained

Question 5:

In a clock having a circular scale of twelve hours, when time changes from 7:45 A.M. to 7:47 A.M., by how many degrees the angle formed by the hour hand and minute hand changes?

a) 10
b) 11
c) 12
d) 15
e) None of these

Answers and Solutions for CAT Questions Based Clock:

Solutions:

Since the watch has to show correct time as 9, when it looses 12 hours.
Time taken to lose 5 minutes = 1 hour.
Time taken to lose 12 hours = 12*60/5 = 144 hours = 6days
Starting from Wednesday, after 6 days it would be Tuesday 7th September.
After Tuesday 7th September, Monday (13 th September) would occur after further 6 days.

The digits on the clock will be in an ascending order from left to right at 12:34.
So, the required time difference will be 7*60 + 4 + 34 = 458 minutes.

Speed of X = 50/5 = 10 m/s
Speed of Y = 40/5 = 8 m/s
Time taken by Y to finish the race = 50/8 = 6.25 s
It is now known that the faulty clock lost time and has shown 6s instead of 6.25s for Y.
Similarly the time taken by Z = 3 * 6.25/6 = 3.125s
Speed of Z = 50/3.125 = 16 m/s.

In a normal watch, the minute hand crosses the hour’s hand after every 1 hour 5 minutes and 27 seconds.
So, the third time the hour’s hand crosses the minute’s hand is after 3 hours 16 minutes and 21 seconds.
In this watch, the time taken for this to happen is 3 hours 18 minutes and 15 seconds.
Hence, the watch loses 1 minute and 54 seconds after every 3 hours 18 minutes and 15 seconds.
18 minutes and 15 seconds = 1095 seconds = 1095/3600 $$\approx$$ .304 hours.
=> 3 hours 18 minutes and 15 seconds = 3.304 hours
So, time lost in a day is $$1\frac{54}{60}*\frac{24}{3.304} = \frac{114}{60}*\frac{24}{3.304} \approx 13.8$$
So, the time lost by the watch in a day is approximately equal to 13 minutes and 48 seconds.

In 1 hour = $$\frac{360}{12} = 30°$$
and in 1 minute = $$\frac{30}{60} = \frac{1}{2}°$$
In 1 minute = $$\frac{360}{60} = 6°$$
=> Every minute, the angle between the two hands changes by = $$6 – \frac{1}{2} = \frac{11}{2}°$$
$$\therefore$$ From 7:45 A.M. to 7:47 A.M.,i.e. in 2 minutes the angle between the two hands will change by
= $$2 \times \frac{11}{2} = 11°$$