Mathematics: Tips for Solving Calender and Clock Problems for Competitive Exams

Tips for Solving Calender and Clock Problems

To solve the problems based on Calendar, we should keep these informations in mind.

• ( i ) Normally an year contains 365 days i.e., 52 weeks and a day. 
• ( ii ) But a leap year contains 366 days i.e., 52 weeks and two days because February of a leap year contains 29 days.
• ( iii ) If an year is exactly divided by 4, it is a leap year. 
• ( iv ) In an year, January, March, May, July, August, October and December contains 31 days. 
• ( v ) While, April, June, September and November contains 30 days.
• ( vi ) February contains 28 days but in a leap year, it contains 29 days.
• ( vii ) A calender year starts with January and ends with December.
• ( viii ) A financial year starts with 1st April and ends with 31st March.
• ( ix ) Generally, Sunday is the first day of a week.
• ( x ) After 7 days i.e., after a week a day repeats itself. Example, if 11th July is Thursday, then 18th July will also be Thursday.

To Solve the Problems Based on Time(Clock) , we Should keep these information in mind.

• ( i ) In each hour, only once both hands of a clock (minute and hour hand) face same direction and also only one time they face opposite directions. When both hands are opposite to each other the gap is of 30 min between them.

• ( ii ) In a minute, the hour hand moves by 0.5° and the minute hand moves by 6°.

• ( iii ) In each hour, the minute hand covers more distance of 55 min in comparison to the hour hand.

• ( iv ) In 12 hour, both hands of a clock (minute and hour hand) face same direction in 11 times and 24 hours they face same direction in 24 times.

• ( v ) In 12 hour, both hands of a clock (minute and hour hand) face opposite direction in 11 times and 24 hour they face same direction in 24 times.

• ( vi ) In each hour, 2 times both hands (minute and hour hand) makes right angle when both hands make right angle the gap is of 15 minute between them.

• ( vii )In 12 hour, both hands of a clock (minute and hour hand) means right angle in 22 times and 24 hours they make right angle in 44 times.

Sample Problems:

1) If 3rd January 2010 was Thursday, what day will be 3rd February 2010 ?

Solution:
As, we know a day repeats itself after a week. Hence, after 3rd January 2010, again on 10th, 17th, 24th and 31st January, it will be Thursday.

• 1st February will be Friday.
• 2nd February will be a Saturday.
• 3rd February will be Sunday.

Ans:- Sunday

2) In 40 min, what angle will the hour hand move at ?

Solution: In a min, hour hand moves at 0.5°. In 40 min, hour hand moves at 0.5 x 40 = 20°

Ans:- 20°

3) If 4th July 2010 was Sunday, what day will be 5th July 2011 ?

Solution: 
As, we know an year contains 52 weeks and a day repeats itself 7 days.
4th July 2010 was Sunday.
4th July 2010 - 4th July 2011 is a period of 365 days.

i.e., 52 weeks and a day.

3rd July 2011 will also be Sunday.

5th July 2011 will be Tuesday.