Clocks and Calendar Quiz-1

Solution: On 31st December, 2005 it was Monday.

Number of odd days from the year 2005 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.

Thus, on 1st Jan, 2009 it is Saturday.

 

Solution: In 100 years there are 5 odd day, which results in Friday as the last day.

In 200 years there are 5*2 = 10; 3 odd days, which results in Wednesday as the last day.

In 300 years there are 5*3 = 14, 1 odd day, which results in Monday as the last day.

In 400 years there are 0 add days, which results in Sunday as the last day.

After 400 years the cycle is again repeated.

Therefore, the last days of the century can never be Tuesday, Thursday, and Saturday.

Solution: count days from January to March as:

31+29+31+30=121=17*7+2

The day on 1^st May will be Monday+2=Wednesday

Solution: I am 40 weeks 43 days younger to Shashank. 43 days can be written as 7*6+1. Therefore, day on my birthday must have been Monday+1=Tuesday.

Solution:

Repetition of leap year ===> Add +28 to the Given Year.

Repetition of non leap year

Step 1 : Add +11 to the Given Year. If Result is a leap year, Go to step 2.

Step 2:  Add +6 to the Given Year.

 

Solution :

Given Year is 1993, Which is a non leap year.

Step 1 : Add +11 to the given year (i.e 1993 + 11) = 2004, Which is a leap year.

Step 2 : Add +6 to the given year (i.e 1993 + 6) = 1999

Therfore, The calendar for the year 1993 will be same for the year 1999

Solution: The hands of the clock coincide 11 times in 12 hours. So in day it coincides 22 times.

Correct Option: B

Solution: The time difference between 9 o’clock and 3 o’clock is 6 hours.

Angle traced by hour hand in 6 hours =

180 deg

Solution:

The angle traced by minute hand in one minute = 6°

Therefore, the angle traced by minute hand in 25 minutes = 25*6 = 150°

The angle traced by hour hand in one hour = 30°

Therefore, the angle traced by hour hand in 11 hour = 11*30 =330°

However, since the time is 11:45 the hour hand is not exactly at 11. Instead it lies somewhere between 11 and 12. Since the time is 11:45 and 45 minutes is ¾ of an hour; therefore, the exact angle it subtends:

330° + ¾ * 30°

330°+22.5°

352.5°

The angle between minute hand and the hour hand can be determined by:

352.5° – 150° = 202.5°

Solution: In 60 minutes the minute hand covers 360°. Therefore, angles of the minute hand can be denoted as 6n, where n depicts the number of minutes past midnight.

Similarly, in 60 minutes the hour hand moves 30 degrees, that is, the angle of the hour hand can be given by 0.5n.

The hands starts to move at midnight and the first time they subtend a right angle can be given by:

6n = 0.5n + 90

5.5n = 90

n = 16 4/11

The next time the right angle is formed when the minutes hand has gained 180 degrees on the hour hand,

6n = 0.5n +270

5.5n = 270

n = 49 1/11

For every 180 degree the minute hands gain on hour hand will be one right angle:

• 49 1/11 – 16 4/11


• 32 8/11

• 1440 / (32 8/11) = 44


• Every in every 24 hours the minute hand and hour hand forms right angles 44 times.

Explanation:-

360/12 = 30 degrees per major division (hours).

360/60 = 6 degrees per minor division (minutes).

At 10:10, the minute hand is at the 2-hour position, 60 degrees clockwise from 12.

The hour hand moves 360 degrees in 12 hours, so it moves 360 / 12 / 60 degrees per minute, or 0.5 degrees per minute. (check: 60 min x 12 hours x 0.5 = 360)

The hour hand is at the 10 position at 10 o’clock. By 10:10 it has moved 0.5 x 10 degrees closer to 12, so at 10:10 it is at 60 - 5 = 55 degrees counterclockwise from 12.

60 + 55 degrees is 115 degrees.