ODD DAYS : Number of days more than the complete of weeks in a given period is the number of odd days during that period.
LEAP YEAR : Every year which is divided by 4 is called a leap year. E.g. 1992,1996,2001,2008 etc
CLOCK : The face or dial of a watch is a circle whose circumference is divided into 60 equal parts called minute spaces.
A clock has two hands, the smaller one is called the hour hand or short hand while the larger one called the minute hand or long hand.
Results
#1. On what dates of July 2004 did Monday fall ?
On what dates of July 2004 did Monday fall ?
Let us find the day on 1st July,2004
2000 years have 0 odd day. 3 ordinary years have 3 odd days.
Jan (plus) Feb. (plus) March (plus) April (plus) May (plus) June (plus) July
31 (plus) 29 (plus) 31 (plus) 30 (plus) 31 (plus) 30 (plus) 1
=183 days
=(26 weeks (plus) 1 day)
=1 odd day
Total number of odd days= (0 (plus) 3 (plus) 1) odd days
=4 odd days
1st Monday in July 2004 was on 5th July
5th, 12th, 19th and 26th.
#2. What was the day of the week on 16th April 2000 ?
What was the day of the week on 16th April 2000 ?
16th April, 2000= (1999 years (plus) Period from 1st Jan.,2000 to 16th April, 2000)
Counting of Odd days :
1600 years have 0 odd day. 300 years have 1 odd day.
99 years = (24 leap years (plus)75 ordinary years)
= [(24*2) (plus)(75 * 1)] odd days
=123 odd days
(17 weeks (plus)4 days)
= 4 odd days
Jan (plus) Feb. (plus) March (plus) April
31 (plus) 29 (plus) 31 (plus) 16
= 107 days
= (15 weeks (plus)2days)
=2 odd days
Total number of odd days = (0 (plus) 1 (plus) 4 (plus) 2)
odd days = 7 Odd days
0 odd day
The required day was ‘Sunday’
#3. Today is Friday. After 62 days, it will be :
Today is Friday. After 62 days, it will be :
Each day of the week is repeated after 7 days. so after 63 days, It will be Friday.
Hence, after 62 days, it will be Thursday.
#4. On what dates of April 2001 did Sunday fall ?
On what dates of April 2001 did Sunday fall ?
Find the day on 1st April, 2001, 2000 years contain 2 odd days
Jan (plus) Feb (plus) March (plus) April
31 (plus) 28 (plus) 31 (plus) 1= 91 days
= 13 weeks 0 day
= 0 odd day
Sunday fell on 1st, 8th,15th,22nd and 29th of April 2001.
#5. The First Republic Day of India was celebrated in 26th January,1950.It was:
The First Republic Day of India was celebrated in 26th January,1950.It was:
26th Jan., 1950=(1949 years (plus) period from 1st jan., 1950 to 26th Jan., 1950)
1600 Years have 0 odd day. 300 Years have 1 odd day.
49 years = (12 leap years (plus) 37 ordinary Years)
=[(12 *2) (plus)(37 * 1) ] odd days =61 odd days
=5 odd days
Number of days from 1st Jan. to 26 th Jan.=26=5 Odd days
The required day was ‘ Thursday’
#6. January 1, 2004 was a Thursday. What day of the week lies on Jan 1, 2005 :
January 1, 2004 was a Thursday. What day of the week lies on Jan 1, 2005 :
The year 2004 being a leap year it has 2 odd days.
So, first day of 2005 will be 2 days
beyond Thursday and so it will be Saturday
#7. On 8th March, 2005, Wednesday falls. What day of the week was it o 8th March, 2004 ?
What was the day of the week on 28th May, 2003 ?
The year 2004 being a leap year, it has 2 odd days.
So, the days on 8th March, 2005 will two days beyond the day on 8th March, 2004
But,8th March, 2005 is Wednesday
So,8th March 2004 is Monday
#8. What was the day of the week on 28th May, 2003 ?
What was the day of the week on 28th May, 2003 ?
2000 year have 2 odd days
The years 2001 and 2002 have (1 plus 1 ) = 2 odd days
Jan. 31 (plus) Feb 28 (plus) March 31 (plus) April 30 (plus) May 28 (plus)
=148 days = 21 weeks plus 1 day = 1 odd days
Total number of odd days = (2 plus 2 plus 1 plus ) = 5
The required day was ’Friday’
#9. At 3.40 the hours hand and the minutes hand of a clock from an angel of :
At 3.40 the hours hand and the minutes hand of a clock from an angel of :
Angle traced by hour hand in 12 hrs = 360°
Angle traced by it in 11/3 hrs = (360/12*11/3)° = 110°
Angle traced by minute hand in 60 min = 360°
Angle traced by it in min =(360/60*40) = 240°
∴ Required angle (240 – 110)°
= 130°
#10. A clock is started at noon. By 10 minutes past 5, the hour had has turned through :
A clock is started at noon. By 10 minutes past 5, the hour had has turned through :
Angle traced by hour hand in 12 hrs = 360°
Angle traced by hour hand in 5 hrs 10 min i.e 31/6 hrs
= (360/12*31/6)°
= 155°
#11. How many times do the hands of a clock coincide in a day ?
How many times do the hands of a clock coincide in a day ?
The hands of a clock coincide 11 times in every 12 hours
∴The hands coincide 22 times in a day
#12. How many times are the hands of a clock at right angle in a day ?
How many times are the hands of a clock at right angle in a day ?
In 12 hours, they are at right angles 22 times.
∴ in 24 hours they are at right angle 44 times.
#13. How many times in a days the hands of a clock are straight ?
How many times in a days the hands of a clock are straight ?
In 12 hours, the hands coincide or are in opposite direction 22 times
In 24 hours the hands coincide or are in opposite direction 44 times a day
#14. An accurate clock shows 8 of clock in the morning through how many degrees will the hour hand rotate when the clock shows 2 of clock in the afternoon ?
An accurate clock shows 8 of clock in the morning through how many degrees will the hour hand rotate when the clock shows 2 of clock in the afternoon ?
Angle traced by the hour hand in 6 hours = (360/12*6)°
= 180°
#15. The angle between the minutes hand and hour hands of a clock when the minutes is :
The angle between the minutes hand and hour hands of a clock when the minutes is :
Angle traced by hour hand in 17/2 hrs = (360/12*17/2)°= 255
Angle traced by ,min hand in 30 min = ( 360/60*30)° = 180
∴ Required angle = ( 255 – 180)°
= 75
#16. At what time between 5.30 and 6 will the hands of a clock be at right angles ?
At what time between 5.30 and 6 will the hands of a clock be at right angles ?
At 5 O’clock, the hands are 25 min. spaces apart.
55 min. spaces are gained in 60 min
40 min. spaces are gained in (60/55 * 40) min.
43 ⁷⁄₁₁ min. past 5
#17. How many time in a day, the hands of a clock are straight ?
How many time in a day, the hands of a clock are straight ?
In 12 hours, the hands coincide or are in opposite direction 22 times
In 24 hours, the hands coincide or are in opposite direction 44 times a day
#18. How many times are the hands of a clock at right angle in a day ?
How many times are the hands of a clock at right angle in a day ?
In 12 hours, they are at right angles 22 times.
In 24 hours, they are right angles 44 times.
#19. At what time between 9 and 10 O'clock will the hands of a watch be together?
At what time between 9 and 10 O’clock will the hands of a watch be together?
45 min are gained in (60/55 *45)min.
=49 ¹⁄₁₁ min past 9
#20. The angle between the minute hand and the hour hand of a clock when the time is 8.30 is:
The angle between the minute hand and the hour hand of a clock when the time is 8.30 is:
Angle traced by hour hand in 17/2 hrs=(360/12*17/2)°=225
Angle traced by min. hand in 30 min.= (360/60*30)°=180
required angle=(255-18)
75°