Q: A clock is set right at 6 am. The clock losses 16 min in 24 h. What will be true time. if the clock indicates 11 pm on 4th day?

Time from 6 am on a day to 11 pm on 4th day = 89 h Now, 23 h 44 min of this clock = 24 h of correct clock 89 h of this clock = 24 x (15/356) x 89 h of correct clock = 90 h of correct clock ∴ Correct time will be 12 o' clock (mid-night).

Question 1

An accurate clock shown 8 O' clock in the morning through how many degrees will the hour hand rotate when the clock shows 2 O' clock in the afternoon?

Accepted Answer

Since, in a clock hour hand completes an angle of 360° in 12 h and there is a gap of 6 h between 8 am and 2 pm, so in 6 h, hour hand completes an angles of 180°.

Question 2

If the seventh day of a month is three days earlier than Friday, what day will be on the nineteenth day of the month?

Accepted Answer

Three days earlier than Friday means Tuesday. So, 7th day of month will be Tuesday. 14th day of month will be Tuesday. 19th day of month will be Sunday.

Question 3

If a month in an year start with Monday, then the date of the fourth day after the second Saturday in that month, will be?

Accepted Answer

1st day of month is Monday. 6th day of month is Saturday. 13th day of month is second Saturday. 17th day is the fourth day after second Saturday.

Question 4

In a clock, the angle between the hour hand and minute hand at 5 h 10 min, is?

Accepted Answer

The angle between hour hand and minute hand at 5 O'clock = 5 x 30° = 150° Minute hand move in 10 min = 2 x 30° = 60° Hour hand move in 10 min = 30°/6 = 5° ∴ Angle between hour hand and minute hand at 5 h 10 min = 150° - 60° + 5deg; = 95°

Question 5

The director came to the office to attend a meeting at 15 min past 12 and he came 25 min before his steno who in turn was late by 30 min to the meeting. At what time was the meeting supposed to start?

Accepted Answer

Director came at 12 : 15. Steno came at 12 : 40. Since, steno was late by 30 min to the meeting. ∴ Meeting time 12 : 10

Question 6

When the time in the wall clock in 3:25 pm, the acute angle between the hour hand and minute hand is?

Accepted Answer

Since, angle between two number is 360°/12 = 30° When the time is 3:25 pm, the minute hand will be at 5 and will have moved 60° from 3 and hour hand would be between 3 and 4 it will move 30° in 60 min and so in 25 min it would have moved 30 x 25/60 = 12.5° So, angle between two hand will be 60 - 12.5 = 47.5°

Question 7

A clock is set to show the correct time at 7 am Monday. The clock losses 15 min in 24 h. What will be the true time when the clock indicates 6 am on the following Friday?

Accepted Answer

Time from 7 am on a day to 6 am after 3 days is 95 h. Now , 23 h 45 min of the clock in question = 24 h of correct clock i..e., 95/4 h of the clock in question = 24 h of correct clock ∴ 95 h of the clock in question = (24 x 4/95 x 95) h of correct clock = 96 h So, the correct time is 96 h from 7 am, Monday, ie., 7 am, Friday.

Question 8

At what time between 9 o'clock and 10 o'clock, will the hands of a clock be in the same straight line but not together?

Accepted Answer

At 9 o'clock, the hour hand is at 9 and the minute hand is at 12. it means that the two hands are 15 min spaces apart .To be in the same straight line (but not together ), they will be 30 min space apart . ∴ The minute hand will have to gain (30 - 15) = 15 min space over the hour hand . As we Know, 55 min spaces are gained in 60 min. ∴ 15 min will be gained in (60/55 x 15) min = 180/11 = 164 /11 min Hence, the hands will be in the same straight line but not together at 164/ 11 min past 9.

Question 9

At what time between 2 o'clock and 3 o'clock, will the hands of a clock point in opposite directions?

Accepted Answer

Given that n = 2 and (n + 1) = 3(n < 6) The hands will be at the same straight line at ⇒ (5n + 30) x 12/11 min past n. ⇒ (5 x 2 + 30 ) x 12/11 min past 2. ⇒ (10 + 30) x 12/11 min past 2. ⇒ 40 x 12/11 min past 2. ⇒ 480/11 min past 2.

Question 10

A clock is set right at 6 am. The clock losses 16 min in 24 h. What will be true time. if the clock indicates 11 pm on 4th day?

Accepted Answer

Time from 6 am on a day to 11 pm on 4th day = 89 h Now, 23 h 44 min of this clock = 24 h of correct clock 89 h of this clock = 24 x (15/356) x 89 h of correct clock = 90 h of correct clock ∴ Correct time will be 12 o' clock (mid-night).

Question 11

A clock is set right at 9 pm. The clock gains 10 min in 24 h. What will be true time, when the clock indicates 2 pm on the following day?

Accepted Answer

Time from 9 pm in a day to 2 pm on the following day = 29 h. 24 h 10 min of this clock = 24 h of the correct clock or 145/6 h of this clock = 24 h of the correct clock 29 h of this clock = 24 x (6/145) x 29 h of the correct clock = 28 h 48 min of correct clock ∴ The correct time is 28 h 48 min after 9 am. This will be 48 min past 1.

Question 12

The minute hand of a clock overtakes the hour hand at intervals of 70 min of the correct time. How much in a day does the clock gain or loss?

Accepted Answer

Given that, time to overtake N = 70 min The required result = [(720/11) - N) ] x [(60 x 24)/N) min = [(720/11) - 70) ] x [(60 x 24)/70) min = [(720 - 770) / 11] x [(60 x 24) / 70] min = - (50/11) x [(6 x 24)] / 7 min = -7200/77 min -ve sign indicates that there is a loss.

Question 13

How much does a watch gain per day, if its hand coincide every 64 min?

Accepted Answer

If the minute hand of a clock overtakes the hour hand at interval N min of the correct time, then clock losses or gains by The required result = [(720/11) - N) ] x [(60 x 24)/N) min Positive for gain and negative for loss Here, N = 64 required time = [(720/11) - 64) ] x [(60 x 24)/64) min = 328/11 min

Question 14

January 3, 2007 was Wednesday. What day of the week fell on January 3, 2008?

Accepted Answer

The year 2007 is an ordinary year, so it has 1 odd day. 3rd day of the year 2007 was Wednesday. ∴ 3rd day of the year 2008 will be one day beyond the Wednesday. Hence, it will be Thursday.

Question 15

January 3, 2008 was Friday. What day of the week fell on January 3, 2009?

Accepted Answer

The year 2008 is a leap year, so it has 2 odd days, 3rd day of the year 2008 was Friday. ∴ 3rd day of the year 2009 will be 2 days beyond the Friday. Hence, the required answer is Sunday.

Question 16

If 5th March, 1999 was Friday, what day of the week was it on 9th March 2000?

Accepted Answer

5th March, 1999 is Friday. Then, 5 March 2000 = Friday + 2 = Sunday (2000 is leap year and it crosses 29th feb 2000, so 2 is taken as odd day} ∴ 5th March 2000 = Sunday Then, 9th March 2000 = Thursday.

Question 17

On 6th March, 2005, Monday falls. What was the day of the week on 7th March, 2004?

Accepted Answer

6th March 2005 = Monday. Then, 6th March 2004 = Monday - 1 days = Sunday. (2004 is a leap year but it does not cross 29th February of 2004, so only 1 is taken as odd day). 6th March 2004 = Sunday 7th March 2004 = Monday.

Question 18

What was the day of the week on 2nd Jan, 2010, If it was Sunday on 1st Jan, 2006?

Accepted Answer

On 31 st December, 2005 it was Saturday, Number of odd days from the year 2006 to the year 2009 = 1 odd day of 2006 + 1 odd day of 2007 + 2 odd days of 2008 (leap year) + 1 odd day of 2009 = 1 + 1 + 2 + 1 = 5 ∴ On 31st December 2009, it was Thursday Thus, on 2nd January 2010, it was Saturday .

Question 19

At what time between 7 and 8 O'clock will the hands of a clock be at right angle?

Accepted Answer

Question 20

At what time between 5 and 6 O'clock are the hands of a clock 3 minutes apart?

Accepted Answer

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