### CALENDARS & CLOCKS

1. How many odd days are there in 95 days?

1) 4                2) 5                3) 3                   4) 6

2. If 6th February 2012 is Sunday, then 14th Nov in 2018 is on which day?
1) Friday              2) Wednesday              3) Saturday             4) Tuesday

3. If today is Friday, then what day was the 124th day back from today?
1) Monday              2) Wednesday              3) Friday             4) Sunday

4. What is the next leap year after 2096?
1) 2100              2) 2108               3) 2102            4) 2104

5. How many odd days are there in a leap year?
1) 1               2) 2               3) 0              4) 4

6. How many odd days are there in a non leap year?
1) 0              2) 4               3) 2                 4) 1

7. How many odd days are there in the year 1974?
1) 0            2) 1                3) 2                4) 4

8. How many odd days are there in the year 2100?
1) 0                2) 1                3) 2               4) 4

9. How many odd days are there in the year 1956?
1) 0               2) 1            3) 2           4) 4

10. How many odd days are there in one year and twenty days?
1) 0         2) 1         3) 4         4) Cannot be determined

11. How many odd days are there from 15th January to 26th August (including both the days) in a leap
year?
1) 1      2) 2       3) 4        4) cannot be determined

12. How many odd days are there from 15th August to 26th January (including both the days) in a year?
1) 0       2) 6        3) 4            4) Cannot be determined

13. If 13th march in a particular year is Tuesday, then 19th October in that year is on
1) Friday       2) Saturday       3) Sunday        4) Monday

14. If 12th January in a particular year is Sunday, then 26th December in that year is on
1) Sunday          2) Friday            3) Tuesday           4) Cannot be determined

15. If 20th November in a particular year is Tuesday, then 16th March in that year is on
1) Sunday           2) Friday            3) Thursday            4) Cannot be determined

16. If the first day of the year 2015 is Wednesday, then what is the first day of the year 2019?
1) Friday           2) Saturday            3) Monday           4) Tuesday

17. If the first day of the year 2004 is Wednesday, then what is the first day of the year 2012?
1) Saturday         2) Friday            3) Sunday            4) Tuesday

18. How many odd days are there in the first 100 years?
1) 2               2) 3             3) 5              4) 6

19. How many odd days are there in the first 1400 years?
1) 0              2) 1                3) 5                4) 3

20. How many odd days are there in the first 2700 years?
1) 0             2) 1              3) 3                 4)     5

21. If 14th March 2005 is Saturday, then 14th March 2007 is on which day?
1) Friday              2) Sunday            3) Monday               4) Thursday

22. If 28th January 2006 is Saturday, then 28th January in 2009 is on which day?
1) Wednesday                2) Friday                   3) Sunday              4) Tuesday

KEY:  1-1; 2-4; 3-4; 4-4; 5-2; 6-4; 7-2; 8-2; 9-3; 10-4; 11-1; 12-4; 13-1; 14-4; 15-2; 16-3; 17-1; 18-3; 19-4; 20-2;
21-3; 22-1.

SOLUTIONS

1. Number of odd days in 95 days.
95/7 = 13 complete weeks + 4 odd days
A: 1

2. If 6th February 2012 is Sunday, first let us find out 14th November in 2012 is on which day.
Number of odd days from 6

February 2012 to 14th November 2012
Month: Feb + March + Apr + May + June + July + Aug + Sep + Oct + Nov.
Odd days: 2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 0
23/7 = 2 odd days.
From 6th February 2012 to 14th November 2012 there are two odd days, hence 14th November 2012
is two days to Sunday i.e. Tuesday.
From 14th November 2012 to 14th November 2018, there are six years. Among these six years there is
one leap year and five non leap years. 7
i.e: (1 × 2 + 5 × 1) ⇒ (2 + 5) = 7/7 = 0 7
odd days in these six years.
Hence, 14th November 2018 will be on the same day as 14th November 2012 i.e. Tuesday.
A: 4

3. Number of odd days in 124 days

If today is Friday then five days back from today was sunday
A: 4

4. For every four years a leap year will come, 2096 + 4 = 2100 but 2100 is a century year and is not
divided by 400. So, 2100 is not a leap year. Hence, the next leap year after 2096 will be 2104.
A: 4

5. A leap year will have 366 days.
Number of odd days in a leap year
366/7 = 2 odd days.
Hence a leap year will have two odd days.
A: 2

6. A non leap year will have 365 days
Number of odd days in a non leap year
365/7 = 1odd day
Hence, non leap year will have only one odd day.
A: 4

7. As 1974 is not divided by 4, it is a non leap year. A non leap year will have only one odd day.
A: 2

8. The year 2100 is a non leap year, so 2100 will have only one odd day.
A: 2

9. The year 1956 is a leap year. So 1956 will have two odd days .
A: 3

10. The given year is a leap year or non leap year is not clearly given. Hence number of odd days in one
year and twenty days cannot be determined.
A: 4

11. Number of odd days from 15th January to 26th August in a leap year
Months: Jan + Feb + March + April + May + June + July + Aug
Days (odd days): 17(3) + 29(1) + 31(3) + 30(2) + 31(3) + 30(2) + 31(3) + 26(5)
Total odd days  = 22/7  = 1 odd day.
A: 1

12. As the year is a leap year or not is not clearly given. So, number of odd days cannot be determined.
A: 4

13. Number of odd days from 13th March to 19th October
Months: March + April + May + June + July + Aug + Sep + Oct
odd days: 4 + 2 + 3 + 2 + 3 + 3 + 2 + 5
Total odd days =
Three days to Tuesday day is Friday.
A: 1

14. As the Year is a leap year or not is not clearly given So, number of odd days cannot be determined.
A: 4

15. Number of odd days from 20th November to 16th March
Months: Nov + Oct + Sep + Aug + July + June + May + April + March
Odd days: 5 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 2
25/7 = 4 Odd days
As 20th November is Tuesday then 16th March will be 4 days back to Tuesday i.e. Friday.
A: 2

16. There are four years in between 1st January 2015 to 1st January 2019. In these 4 years, there are 3 non
leap years and 1 leap year.
3 non leap years will have − 3 × 1 = 3
1 leap year will have     −   1 × 2 = 2
= 5
Hence, there are five odd days in these four years.
As 1st January 2015 is Wednesday then 1st January 2019 will be five days to Wednesday i.e. Monday.
A: 3

17. There are eight years between 1st January 2004 to 1st January 2012. In these eight years there are six
non leap years and two leap years.
A leap year will have two odd days = 2 × 2 = 4
A non leap year will have one odd day = 6 × 1 = 6
Hence, there are ten odd days in these eight years = 10/7 = 3 odd days
As 1st January 2004 is Wednesday then 1st January 2012 will be three days to Wednesday i.e. Saturday .
A: 1

18. In the first hundred years, there are 24 leap years and 76 non leap years,
A leap year will have two odd days = 24 × 2 = 48
A non leap year will have one odd day= 76 × 1 = 76
total odd days = 124
i.e.
Hence, there are five odd days in the first 100 years.
A: 3

19. 1400 years = 400 × 3 + 200 years
0 × 3 + 3 × 1 = 3 odd days
(100 years − 5 odd days
200 years − 3 odd days
300 years − 1 odd day
400 years − 0 odd day)
A: 4

20. 2700 years = 400 × 6 + 300 × 1
0 × 6 + 1 × 1 = 1 odd day
Hence, there is one odd day in the first 2700 years.
A: 2

22. There are three years between 28th January 2006 to 28th January 2009. In these three years there is one
leap year and two non leap years. A leap year will have two odd days and a non leap year will have one
odd day (i.e. 1 × 2 + 2,× 1 = 4). So, there are four odd days. If 28th January 2006 is Saturday then 28th
January 2009 will be four days to Saturday i.e. Wednesday.
A: 1

CLOCKS

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.

Posted Date : 07-02-2021