14-07-2021 Answers

1. At 6 a clock ticks 6 times. The time between first and last ticks is 15 seconds. How long does it tick at 12 ?

Answer: 33 seconds

Solution: When  the clock ticks 6 times  T T T T T T, there will be 5 intervals.

So duration for each interval = 15/5 = 3s; When it is 12, there will be 11 intervals and hence duration = 11*3 = 33.

2. A watch gains 10 seconds in 30 minutes and was set right at 1 AM. What time will it show at 4 PM on the same day?

Answer: 4:05 PM

Solution: The watch gains 10s in 30 mins. That is 20s in 1 hr.

From 1 AM to 4 PM on the same day, time passed is 15 hours.

In 15 hours, the watch would have gained 15*20 seconds = 5 mins. So, when the correct time is 4 PM, the watch would show 4:05 PM

3. What is the time now if 2 hours later it would be half as long until midnight as it would be if it were an hour later?

Answer: 9 PM

Solution: After x+2 hours, let it be y time till midnight. Then after x+1 hours it is 2y time till midnight. Hence  12-(x+2) = y and 12-(x+1) = 2y.

=> 24 -2x - 4 = 12 -x-1; Solving x=9

4. If time at this moment is 11 A.M., what will be the time 47999999992 hours later?

Answer: 3 AM

Solution: 48000000000 hours later it will be 11 A.M (exactly divisible by 24 hours).

8 hours before (48000000000-47999999992) 11 A.M is 3 A.M.

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

Answer: 10:23:20 PM

Solution: The watch gains 5s in 3 mins. So, 100 seconds in 1 hr.

From 8 AM to 10 PM on the same day, time passed is 14 hrs.

In 14 hrs, the watch would have gained 1400 seconds = 23 mins 20s; So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

6. An aircraft takes off from A (72° N Lat, 40° E Long) at 2.00 AM local time to B (32° N Lat, 50° W Long). If the flying time is 10 hours what is the local time of landing at B?

Answer: 6:00 AM

Solution: The destination place is 90° west to the starting place. Hence the time difference between these two places is 6 hrs (24hr*90/360).

When the flight landed, the time at the starting place is 12 noon (2 AM + 10 hours). The time zones go back if going westwards. Hence, the time at the destination place is 12 noon – 6 hours = 6:00 AM

7. What is the angle between the hands of the clock at 7:20 in a 12 hour clock?

Answer: 100 degrees

Solution: Hour hand movement = 7*30 + 20*1/2 =  220°

Minute hand movement = 20 * 6 = 120°

Hence angle between = 220 - 120 = 100°

8. A student started taking a test between 3 pm and 4 pm. When he completed the test at a time between 4 pm and 5 pm, the position of the hands were interchanged when compared to the time of starting the test. For how many hours did the test last?

Answer: 12/13 hours

Solution: Let initial angular difference between hour and minute hands be x degrees.

At the completion of test, hour hand will move x degrees.

Minute hand will move (360-x) degrees.

We know that minute hand moves 12 times faster than hr hand. Let the duration of test be for M minutes.

So, M*12*x = M*(360-x), x=360/13. So, hour hand travels 360/13 degrees.

We know, in 1 hour, the hour hand travels 30°

So time taken M = 360/13 *  1/30 = 12/13 hours

9. At 6 a clock ticks 6 times. The time between first and last ticks is 30 seconds. How long does it tick at 12.

Answer: 66 seconds

Solution: When  the clock ticks 6 times  T T T T T T, there are 5 intervals. So duration for each interval = 30/5 = 6s; When it is 12, there are 11 intervals and hence duration = 11 * 6 = 66 seconds.

10. A watch gaining uniformly was 10 minutes slow at noon on Monday and was 15 minutes fast at 2 p.m. on the following Wednesday. When was it correct?

Answer: Tuesday 8 AM

Solution: Duration from Monday noon to Wednesday 2PM = 50 hours. 

Time gained in these 50 hours = 10+15 = 25 mins.

Hence in 1 hour the watch gains = 0.5 mins.

Hence to adjust for the 10 minutes slowness and show right time it needs 10/0.5 = 20 hours. Hence the watch was correct at Tuesday 8AM.

11. A watch gaining uniformly was 8 minutes slow at noon on Wednesday and was 17 minutes fast at 2 p.m. on the following Friday. When was it correct?

Answer: Thursday 4 AM

Solution: Duration from Wednesday noon to Friday 2PM = 50 hours.

Time gained in these 50 hours = 8+17 = 25 mins.

Hence in 1 hour the watch gains = 0.5 mins.

Hence to adjust for the 8 minutes slowness and show right time it needs 8/0.5 = 16 hours.

Hence the watch was correct at Wednesday noon + 16 hours = Thursday Morning 4 AM

12. Find the angle between the hour hand and minute hands of the clock at  5:30

Answer: 15 degrees

Solution: Angle hour hand has moved = 5*30 + 30*1/2 = 165°

Angle minute hand has moved = 30*6 = 180°; So angle between the hands = 15

13. What is the angle between the minute and hour hand at 11:30?

Answer: 165 degrees

Solution: Angle between H and M =|(H*30)-(M*11)/2)|, where H is hrs and M is mins.

Angle = |330-(15*11)| = |330-165| = 165°

14. Madan adjusted his watch at 9PM on 20-March-2012 to reflect correct time. There after, the minute hand overtook the hour hand at intervals of 60 minutes. Madan went to the railway station sharp at 8 AM on 21-March-2012 to catch the train at 8AM. Assuming the train is punctual, approximately how long Madan had to wait for the train?

Answer: 1 hour

Solution: In a correct watch the minute hand gains 55 minutes over hour hand in 60 minutes. To overtake, 60 minutes gain is needed. Hence time to overtake in a correct watch = 60 * 60/55 mins.

But as in Madan's watch minute hand overtook in 60 mins, the clock gained = 60*60/55 - 60 = 60(60/55-1) = 60 (5/55) = 60/11 mins.

From 9PM to 8AM it is 11 hours. Hence time gained = 60/11 * 11 = 60 mins; Hence he had to wait for 60 mins or 1 hour.

15. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through

Answer: 155 degrees

Solution: 5 hours 10 minutes = 5 1/6 = 31/6 hours

Degrees = (31/6)*(360/12) = 31 * 5 = 155

16. At what time are the hour and minute hands of a 12 hour clock together between 2 and 3 pm?

Answer: 2h:10m:54s PM

Solution: Between T and T+1 hours on a 12 hour clock, the minutes beyond T hour when the hands will be together is given by the formula 60T/11.

Here T=2, so the hands will be together at 60*2/11 = 10.9090 mins = 10 mins 54s (0.9090 * 60 seconds = 54s)

17. In a 12 hour clock what is the angle between the hands of the clock at 4:40?

Answer: 100 degrees

Solution: In 1 minute, hour hands moves = 360/(12*60) = 0.5°

In 1 hour it moves = 360/12 = 30°

In 1 minute, minute hand moves = 360/60 = 6°

At 4:40, hour hand has moved = 4 hrs * 30° + 40 mins * 0.5° = 140°

Minute hand has moved = 40 mins * 6° = 240°

Angle between the hands = 240-140 = 100

18. At what time are the hour and minute hands of a 12 hour clock together between 6 and 7 pm?

Answer: 6h:32m:43s PM

Solution: Between T and T+1 hours on a 12 hour clock, the minutes beyond T hour when the hands will be together is given by the formula 60T/11.

Here T=6, so the hands will be together at 60*6/11 = 32.7272 minutes = 32 mins 43 seconds approx (0.7272 * 60 seconds = 43 seconds)

19. A flight takes off at 1:00 AM from a place at 22N 20E and landed 8 hours later at a place with coordinates 44N 25W. What was the local time when the plane landed?

Answer: 6:00 AM

Solution: The destination place is 45 degree west to the starting place. Hence the time difference between these two places is 3 hours (24hr*45/360).

When the flight landed, the time at the starting place is 9 AM (1:00 AM + 8 hours).

The time zones go back if going westwards. Hence, the time at the destination place is 9AM - 3 hours = 6:00 AM

20. A clock is started at noon. By 20 minutes past 6, the hour hand has turned through

Answer: 190°

Solution: In 1 hour, the hour hand passes thorugh 30°

In 1 minute, the hour hand passes through 0.5°; So, 6 hours * 30 + 20 mins*0.5 = 180 + 10 = 190°

21. If time at this moment is 9 P.M., what will be the time 23999999995 hours later?

Answer: 4 PM

Solution: After every 24 hours the time is same,

So, 24000000000 - 5 = 23999999995.

Hence, the time will be 5 hrs earlier than the current time; 9 PM - 5 hrs = 4 PM.

22. A watch gains 8 seconds in 40 minutes and was set right at 2 PM. What time will it show at 7 PM on the same day?

Answer: 7:01 PM

Solution: The watch gains 8s in 40 mins. That is 12s in 1 hr.

From 2 PM to 7 PM on the same day, time passed is 5 hours.

In 5 hours, the watch would have gained 5*12 seconds = 1 minute.

So, when the correct time is 7 PM, the watch would show 7:01 PM

23. In yet another planet there were 30 hours in a day and 15 hours covered by hour hand in one complete rotation (half day). An hour still consisted of 60 minutes and six minute spaces between each hour. How many times will the minute hand and hour hand be at right angle in a day?

Answer: 36 times

Solution: As there are 15 hours per half day and six minute spaces per hour, angle covered per minute by minute hand = 360/(6*15) = 4°/min.

Angle covered per minute by hour hand = 360/(15*60) = (2/5)°/min.

Let us assume it takes t mins for the hour and minute hand to have a difference of 90 degrees. Then,

  (4 - 2/5)* t = 90 => t = 25 mins.

For the hands to be at right angle they have to be at 90 and 270 degrees (180 and 360 are not considered as they in the same line). Hence every 50 minutes (2*25 = 50 minutes) the minute and hour hand will be at right angle.

Hence in half day, number of times the minute hand and hour hand will be at right angle = 15 hrs * 60 mins/ 50 mins = 18 times. In a day it is 2 * 18 = 36 times.

24. Choose the two options representing the time at which the hour and minute hands of a 12 hour clock will be at right angle between 7'o clock and 8'o clock.

Answer: 7h:04m:32s, 7h:21m:49s

Solution: Between T and T+1 hours on a 12 hour clock, to find when the hands will be M minutes apart is given by the formula (5T+M)*12/11 and (5T-M)*12/11; When the hands are at right angles, they are 15 mins apart.

Here T=7 and M=15, Hence the required minutes after 7'o clock are 600/11 = 54 mins 32 seconds  and 20*12/11 =  21 mins and 49s; Hence the time can be either 7h:54m:32s or 7h:21m:49s.

25. What is the time in clock, if the reflection of the clock in a mirror shows 9 hours 35 minutes?

Answer: 2 hours 25 minutes

Solution: The mirror image is horizontal flip. Hence for 9 hours 35 minutes, the hour hand will actually be between 2 and 3. The minute hand will be at 25 mins.