**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

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**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:**

**1)** Answer (C)

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.

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**2)** Answer (D)

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.

**3)** Answer(C)

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.

**4)** Answer (B)

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.

**5)** Answer (B)

Angle covered by the hour hand in 12 hours = 360Â°

In 1 hour = $$\frac{360}{12} = 30Â°$$

and in 1 minute = $$\frac{30}{60} = \frac{1}{2}Â°$$

Similarly, angle covered by minute hand in 1 hour = 360Â°

In 1 minute = $$\frac{360}{60} = 6Â°$$

=> Every minute, the angle between the two hands changes by = $$6 – \frac{1}{2} = \frac{11}{2}Â°$$

$$\therefore$$ From 7:45 A.M. to 7:47 A.M.,i.e. in 2 minutes the angle between the two hands will change by

= $$2 \times \frac{11}{2} = 11Â°$$

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