1. A clock is set to show the correct time at 8 a.m. the clock gains 12 minutes in a day. What will be the actual time when this clock shows 8 p.m on the next day?
1) 7 hours 42 min. 2) 8 hours 18 min. 3) 8 hours 20 min. 4) 7 hours 40 min.
2. There are two clocks on a wall, both set to show the correct time at 10 a.m. One clock gains one minute in one hour while the other loses one minute in one hour. By how many minutes do the two clocks differ at 11 p.m. on the same day?
1) 13 min. 2) 18 min. 3) 28 min. 4) 26 min.
3. There are two clocks on a wall, both set to show the correct time at 8 a.m. One clock gains one minute in one hour while the other loses two minutes in one hour. What is the time shown by the clock which is losing two minutes. If the clock which is gaining one minute shows 10 : 14 p.m.?
1) 9 hours 28 min. 2) 10 hours 28 min. 3) 9 hours 46 min. 4) 9 hours 32 min.
4. A watch which gains uniformly was observed to be 10 minutes slow at 6 a.m. today and it was noticed that the watch was 20 minutes fast at 9 p.m. on the next day. When did the watch show the correct time
1) 3 a.m. tomorrow 2) 7 p.m. today 3) 6 p.m. tomorrow 4) 10 p.m. today
5. A watch which gains time uniformly was observed to be 15 minutes slow at 8 a.m. on Sunday and it was noticed that the watch was 25 minutes fast at 4 p.m. on the subsequent Tuesday. When did the watch show the correct time?
1) 8 p.m. Sunday 2) 5 a.m. Monday 3) 6 p.m. Monday 4) 12 noon Monday
6. A watch which loses time uniformly was observed to be 15 minutes fast at 10 a.m. On Monday and it was notice that the watch was 25 minutes slow at 6 p.m. on the subsequent Tuesday. When did the watch show the correct time?
1) 10 p.m. Monday 2) 8 p.m. Monday 3) 4 a.m. Thursday 4) 6 a.m.Tuesday
7. If the clock showing 7 hrs. 35. Then what time dose it shows in the mirror?
1) 5 hours 25 min. 2) 4 hours 35 min. 3) 4 hours 15 min. 4) 4 hours 25 min.
8. If the time seen in a mirror is 4 hrs. 28 minutes then what is the actual time?
1) 8 hours 14 min. 2) 7 hours 32 min. 3) 7 hours 24 min. 4) 7 hours 36 min.
9. A clock strikes once at 1 O'clock, twice at 2 O’clock, thrice at 3 O’ clock and so on. If it takes
12 seconds to strike five times at 5 O’ clock, then, how long (in seconds) does it take to strike eleven times at 11 O'clock?
1) 24 seconds 2) 26 seconds 3) 30 seconds 4) 33 seconds
10. A clock strikes once at 1 O'clock twice at 2 O'clock thrice at 3 O'clock and so on. If it takes 8 seconds to strike nine times at 9 O'clock then, how long (in seconds) does it take to strike six times at 6 O'clock?
1) 5 seconds 2) 10 seconds 3) 12 seconds 4) 15 seconds
11. A clock is set to show the correct time at 6 a.m. The clock gains 12 minutes in a day. What will be the approximate time shown by this clock when the actual time on the next day is 8 p.m.?
1) 7 h. 40 min. 2) 8 h. 19 min. 3) 7 h. 41 min. 4) 8 h. 21 min.
EXPLANATIONS
1. Total number of hours between 8 a.m. today to 8 p.m. the next day is 36 hours. The clock gains 12 min. in 24 hours, in 36 hours it gains 18 min. After gaining 18 min the clock shows 8 p.m. Hence the actual time is 18 min less than 8 p.m. i.e. 7 hours 42 min.
2. In one hour the difference between the two clocks is 2 mins. Total number of hours from 10 a.m. to 11 p.m. on the same day is 13 hrs. In 13 hrs. the difference will be 13 × 2 = 26 minutes.
3. In one hour the difference between the two clocks is 3 mins. The clock which is gaining one minute is showing 10 : 14 p.m. means the clock gained 14 minutes in 14 hrs. (i.e. 8 a.m. to 10 p.m.). In these 14 hrs. the second clock loses 14 × 2 = 28 mins. The second clock shows 28 mins to 10 p.m. i.e. 9 hrs. 32 min.
4. Total number of hours from 6 a.m. today to 9 p.m. the next day is 39 hrs. During these 39 hrs. the clock gained 30 minutes. If the clock gains 10 min. then it will show the correct time. To gain 10 min it takes
10/30 × 39 = 13 h.
After 13 hrs. to 6 a.m. today i.e. 7 p.m. today the clock shows the correct time.
5. Total number of hours from 8 a.m. on Sunday to 4 p.m. the subsequent Tuesday is 56 hrs. In these 56 hrs. the clock gains 40 min (− 15 to + 25). If it gains 15 mins then it shows the correct time. To gain 15 minutes it takes 15/40 × 56 = 21 hrs.
After 21 hrs. to 8 a.m. Sunday i.e. 5 a.m. on Monday the clock shows the correct time.
6. Total number of hours from 10 a.m. on Monday to 6 p.m. Tuesday is 32 hrs. In these 32 hrs. the clock looses 40 mins. (+ 15 to − 25). If it looses 15 mins. then it show the correct time. To loose 15 mins. it 15 takes 15/40 × 32 = 12 hrs. After 12 hrs to 10 a.m.
on Monday i.e. 10 p.m. on Monday it shows the correct time.
7. Actual time and mirror time is always equals to 12 hrs.
Mirror time = 12 - (Actual time)
12 − 7 hrs. 35 min. = 4 hrs. 25 mins.
8. Actual time and mirror time is always equals to 12 hrs.
Actual time = 12 − (mirror time)
12 − (4 hrs. 28 mins.) = 7 hrs. 32 mins.
9. To strike 5 times at 5 O' clock the pendulum in the clock should covers 4 periods.
(Number of periods is always one less than the total number of hours)
For four periods it takes 12 sec.
For 1 period it takes
12/3 = 3 sec.
To strike 11 times at 11 O'clock it has to cover 10 periods.
For 10 periods it takes 10 × 3 = 30 sec.
10. (As explained in Q.No. 9)
In 9 hours there are 8 periods.
To cover 8 periods it takes 8 secs.
Hence, for 1 period it takes 1 sec.
To Strike 6 O'clock, it has to cover 5 periods.
For 5 periods it takes 5 × 1 = 5 sec.
11. Total number of hours between 6 a.m. today to 8 p.m. the next day is 38 hours. The clock gains 12 min. in 24 hours, in 38 hours it gains 19 minutes. When the actual time is 8 p.m. this clock shows 19 min. more i.e. 8 hrs. 19 min.
KEY: 1-1; 2-4; 3-4; 4-2; 5-2; 6-1; 7-4; 8-2; 9-3; 10-1; 11-2.
