Reasoning

Clock

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MEDIUM

At what time between 5:00 and 6:00, both the hands of a clock will make an angle of $95^\circ$ for the first time?

5:55

5:10

5:50

5:30

Explanation

Here $A_1 = 5 \times 30 = 150^\circ$ and $A_2 = 95^\circ$ . For the angle to be formed for the first time, we use the '-' formula. $Minutes = \frac{2}{11}(150 - 95) = \frac{2}{11}(55) = 10$ minutes. Thus the time is 5:10.

MEDIUM

Time in a clock is 3 : 13, what time will be appear in water ?

3 : 17

2 : 17

3 : 23

2 : 13

Explanation

Time in water = 18:30 - 3:13 = 15:17 = 3:17

MEDIUM

If the time in clock is 12:23. What is the time in the mirror?

1:23

12:37

11:37

1:32

Explanation

Mirror Image = 11:60 - 12:23 = 11:60 - 00:23 = 11:37

MEDIUM

Reaching the place of meeting on Tuesday 15 minutes before 08:30 hours I found myself half an hour earlier than the man who was 40 minutes late. What was the scheduled time of the meeting?

08 : 00 hours

08 : 05 hours

08 : 15 hours

08 : 45 hours

Explanation

My arrival time = 08:30 - 15 minutes = 08:15.
I was 30 minutes earlier than the person, so that person arrived at 08:15 + 30 minutes = 08:45.
The person was 40 minutes late, so the scheduled time = 08:45 - 40 minutes = 08:05.

MEDIUM

What will be the acute angle between hands of a clock at 2:30?

105°

115°

95°

135°

Explanation

Angle = |302 - 5.530| = |60 - 165| = 105°

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MEDIUM

At what time between 5 and 5:30, will the hands of a clock be at right angle?

10 10/11 min. past 5

10 9/10 min. past 5

11 10/11 min. past 5

None of these

Explanation

Time = 2/11 * (150 - 90) = 2/11 * 60 = 120/11 = 10 10/11 minutes past 5.

MEDIUM

If on the dial of a clock, we substitute the numbers with the reversed order of alphabets K to V so that 'V' substitutes '5' and 'U' substitutes '6' and the process is continued, then which alphabet will come in place of 11?

Explanation

Given alphabet series: K, L, M, N, O, P, Q, R, S, T, U, V.
Substitution as per question:
5 = V, 6 = U
This is a reversed order.
7 = T, 8 = S, 9 = R, 10 = Q, 11 = P, 12 = O, 1 = N, 2 = M, 3 = L, 4 = K.
Thus, 'P' will come in place of 11.

MEDIUM

A watch which gains uniformly, is 5 min. slow at 8 O'clock in the morning on Sunday, and is 5 min. fast at 8 pm on following Sunday. When was it correct?

20 min. past 7 pm on Tuesday

20 min. past 7 pm on Wednesday

10 min. past 7 pm on Tuesday

10 min. past 7 pm on Wednesday

Explanation

Total time = 7 days 12 hours = 180 hours. Total gain = 10 minutes. To be correct, it needs 5 minutes of gain = 5/10 * 180 = 90 hours. Sunday 8 am + 90 hours = Wednesday 2 am (Note: based on calculation).

MEDIUM

After 9 o'clock at what time between 9 p.m. and 10 p.m. will the hour and minute hands of a clock point in opposite direction?

15 minutes past 9

16 minutes past 9

\frac{4}{11}

minutes past 9

\frac{1}{11}

minutes past 9

Explanation

Formula for opposite direction: $M = \frac{60}{11} \times (H \pm 6)$
Since 9 is greater than 6, we subtract: $9 - 6 = 3$
$M = \frac{60}{11} \times 3 = \frac{180}{11} = 16 \frac{4}{11}$ minutes.
Thus the correct time is $16 \frac{4}{11}$ minutes past 9.

MEDIUM

Only 3, 6, 9 and 12 are marked in a clock. It is placed in front of a mirror in the reverse position. If it is 20:42 in the clock, then what time will be seen in the mirror image of the clock?

8:42

9:48

7:42

10:48

Explanation

First convert the given time in 12 hours format. So we will write 20:42 as 8:42. 17:90 - 8:42 = 9:48.

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MEDIUM

At what time between 5:30 and 6:00, both the hands of a clock will make an angle of $70^\circ$ ?

5:38

5:35

5:40

5:45

Explanation

Here $A_1 = 5 \times 30 = 150^\circ$ and $A_2 = 70^\circ$ . $Minutes = \frac{2}{11}(150 \pm 70)$ . Case 1: $\frac{2}{11}(80) = 14\frac{6}{11}$ minutes. Case 2: $\frac{2}{11}(220) = 40$ minutes. Since the time is asked between 5:30 and 6:00, the correct answer is 5:40.

MEDIUM

If in a clock, the minute-hand overtakes the hour-hand in 70 minutes of correct time, then how much does the clock gain or lose in 77 hours?

5 hours slow

5 hours fast

6 hours slow

6 hours fast

Explanation

Given: Time = 70 minutes; Total time = 77 hours. Formula: $\left[\frac{65\frac{5}{11} - 70}{70}\right] \times 77 = \left[\frac{\frac{720}{11} - \frac{770}{11}}{70}\right] \times 77 = \left[\frac{-50/11}{70}\right] \times 77 = \frac{-50}{11 \times 70} \times 77 = -5$ hours. Since the result is negative, the clock is slow.

MEDIUM

A clock which gains uniformly was 5 minutes slow on Sunday 5 p.m. If it is 7 minutes fast on Tuesday 5 p.m., then when did the clock show the correct time?

Monday 7 p.m.

Monday 6 p.m.

Monday 5 p.m.

Monday 1 p.m.

Explanation

From Sunday 5 p.m. to Tuesday 5 p.m., total time = 48 hours. Formula: $\left[\frac{\text{slow}}{\text{slow} + \text{fast}}\right] \times \text{Total time} = \left[\frac{5}{5+7}\right] \times 48 = \frac{5}{12} \times 48 = 20$ hours. Sunday 5 p.m. + 20 hours = Monday 1 p.m.

MEDIUM

If the two hands in a clock are 3 minutes divisions apart, then the angle between them is:

3°

18°

24°

60°

Explanation

1 minute = 6°. 3 minutes = 3 * 6° = 18°.

MEDIUM

At what approximate time between 4 and 5 am will the hands of a clock be at right angle ?

4:35 am

4:39 am

4:40 am

4:38 am

Explanation

Time = 2/11 * (120 ± 90) = 2/11 * (30) = 60/11 = 5 5/11 min past 4. Or 2/11 * (210) = 420/11 = 38 2/11 min past 4. Approx 4:38 or 4:39. Option B is appropriate.

MEDIUM

Find at what time between 2 and 3 O'clock will the hands of a clock be in the same straight line but not together.

43 6/11 min. past 2

43 7/11 min. past 2

43 3/11 min. past 2

None of these

Explanation

Time = 2/11 * (60+180) = 480/11 = 43 7/11. Seems option B is 43 7/11.

MEDIUM

What is angle made by hour hand in 36 seconds?

3°

120°

10/3°

3/10°

Explanation

Hour hand moves 360° in 12 hours. In 1 hour = 30°. In 60 minutes = 30°. In 1 minute = 0.5°. In 60 seconds = 0.5°. In 1 second = 0.5/60 = 1/120°. In 36 seconds = 36/120 = 3/10°.

MEDIUM

A watch gains 5 seconds in 3 minutes, set right at 8 AM. What time will it show at 10 PM on the same day ?

10 : 27 : 41 AM

8 : 51 : 04 AM

9 : 45 : 15 PM

10 : 23 : 20 PM

Explanation

8 AM to 10 PM = 14 hours. Gains 5 sec in 3 mins. In 1 hour (60 mins) = (5/3)*60 = 100 seconds gain. In 14 hours = 1400 seconds gain = 23 minutes 20 seconds. So 10:23:20 PM.

MEDIUM

At what time between 12:00 and 1:00, both the hands of a clock will make an angle of $110^{\circ}$ for the second time?

12:30

12:45

12:43 \frac{5}{11}

12:45 \frac{5}{11}

Explanation

For the first time: $A_1 = 0^{\circ}, A_2 = 110^{\circ}, \text{Minutes} = \frac{2}{11}(0^{\circ}+110^{\circ}) = 20 \text{ minutes} (12:20)$ . For the second time, $A_2 = 360^{\circ}-110^{\circ} = 250^{\circ}$ . $\text{Minutes} = \frac{2}{11}(0^{\circ}+250^{\circ}) = \frac{500}{11} = 45 \frac{5}{11}$ . Hence at 12:45 $\frac{5}{11}$ .

MEDIUM

From 1 pm to 5 pm, for how many times will both the hands of a clock be in the opposite direction?

3 times

4 times

7 times

8 times

Explanation

The time 6:00 does not occur, so opposite direction happens 4 times.

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