CLOCK AND CALENDER

Reasoning and General Intelligence – CLOCK AND CALENDER

Important Points:
1 min — 6°(min Hand) — ½°(hour Hand)
(i.e. one minute is equal to 6 degree of minute hand, which is also equal to half degree of hour hand)


Both hands coincide once every hour
Both hands coincide 22 times every day
Both hands are in opposite 11 times in 12 hours
Both hands are in Right angles 22 times every 12 hours
Both hands are in right angles 2 times every hour but opposite direct once every hour
If both hands coincide once, they will coincide again after every 65 ⁵/₁₁ minutes
So, if the two hands coincide in time less than 65 ⁵/₁₁ minutes, then clockis too fast else too slow.


The Formula for Clock (M → Minute, H → Hour)
If the hour is less than 6 O'Clock (H<6 o'clock) use this formula
Angle = $\frac{\text{11M}}{\text{2}}$ - 30H

if the hour is more than 6 O'Clock (H>6 o'clock) use this formula
Angle = 30H - $\frac{\text{11M}}{\text{2}}$

CALENDAR
Day Code Sunday - 0 Monday - 1 Tuesday - 2 Wednesday - 3 Thursday - 4 Friday - 5 Saturday - 6 Month Code January - 0 February - 3 March - 3 April - 6 May - 1 June - 4 July - 6 August - 2 September - 5 October - 0 November - 3 December - 5 Century Code Divide the century year with 400 eg. if the year is 1955, then 1900 is the century year which must be divided with 400 Then the code is decided as we got remainder as below: If the remainder is 000 then the code is 6 100 then the code is 4 200 then the code is 2 300 then the code is 0 OR follow the below eg. if the year is 1955, then 1900 is the century year but if you divide the two century digits i.e 19 divided by 4 then the code is decided as we got remainder as below: If the remainder is 0 then the code is 6 1 then the code is 4 2 then the code is 2 3 then the code is 0
FORMULA [Date + MonthCode + Year (Last two digits)* + Leap Year($\frac{\text{LastTwoDigits}}{\text{4}}$=Quotient)]÷7
CONDITIONS FOR CALENDAR REPEATITION If $\frac{\text{Last Two Digits}}{\text{4}}$=0 Then 28years must be added to the Given year If $\frac{\text{Last Two Digits}}{\text{4}}$=1 Then 6years must be added to the Given year If $\frac{\text{Last Two Digits}}{\text{4}}$=2 or 3 Then 11years must be added to the Given year
CLOCK MIRROR IMAGE To find out TRUE TIME or MIRROR IMAGE TIME You have to subtract the given time from 11:60 In case, if the given time is 12:00 or above, keep in mind that 12:00 can also be expressed as 0(zero) Consider that mirror is always placed vertically
CLOCK WATER IMAGE To find out TRUE TIME or WATER IMAGE TIME You have to subtract the given time from 18:30 only if the given time minute is ≤ 30 In case, if the given time minute is > 30, you have to subtract the given time from 17:90. Consider that water is always in horizontal

Questions & Answers with Explaination




If the two hands in a clock are 3 minutes divisions apart, then the angle between them is ______. (A) 3° (B) 18° (C) 24° (D) 60° The right option is B Explaination → Right answer is 18° 1 minute = 6° Therefore, 3 minutes = (3 x 6)/1 = 18°

At what time between 4 and 5 o'clock will the hands of clock be at right angle? (A) 4:40 am (B) 4:38 am (C) 4:35 am (D) 4:39 am The right option is B Explaination → Right answer is 4:38 am

What will be the angle between the hands when the time is 2:30? (A) 105° (B) 115° (C) 95° (D) 135° The right option is A Explaination → Right answer is 105°

In 16 minutes, the minute hand gains over the hour hand by -? (A) 16° (B) 80° (C) 88° (D) 96° The right option is C Explaination → Right answer is 88°

A clock is set right at 1 p.m. If it gains one minute in an hour, then what is the true time when the clock indicates 6 p.m. in the same day? (A) 55 $\frac{\text{5}}{\text{61}}$ minutes past 5 (B) 5 minutes past 6 (C) 5 minutes to 6 (D) 59 $\frac{\text{1}}{\text{64}}$ minutes past 5 The right option is A Explaination → Right answer is 55 $\frac{\text{5}}{\text{61}}$ minutes past 5

Two clocks were set right at noon on Sunday. One gains 2 min and the other loses 3 min in 24 hours. What will be the true time when the first clock indicates 3 pm on Wednesday? (A) 2:38 pm (B) 2:54 pm (C) 2:23 pm (D) 2:48 pm The right option is B Explaination → Right answer is 2:54 pm

At what time between 9’O clock and 10'Oclock will the hands of a clock point in the opposite directions? (A) 16 $\frac{\text{4}}{\text{11}}$ minutes past 9 (B) 16 $\frac{\text{4}}{\text{11}}$ minutes past 8 (C) 55 $\frac{\text{5}}{\text{61}}$ minutes past 7 (D) 55 $\frac{\text{5}}{\text{61}}$ minutes to 8 The right option is A Explaination → Right answer is 16 $\frac{\text{4}}{\text{11}}$ minutes past 9 You can even check it out from answer options

A clock gains 15 minutes per day. It is set right at 12 noon. What time will it show at 4.00 am, the next day? (A) 4:10 am (B) 4:45am (C) 4:20 am (D) 5:00am The right option is A Explaination → Right answer is 4:10 am

Find the exact time between 7 am and 8 am when the two hands of a watch meet? (A) 7 hrs 35 min (B) 7 hrs 36.99 min (C) 7 hrs 38.18 min (D) 7 hrs 42.6 min The right option is C Explaination → Right answer is 7 hrs 38.18 min

At what time between 3 and 4'O clock, the hands of a clock coincide? (A) 16 $\frac{\text{4}}{\text{11}}$ minutes past 3 (B) 15$\frac{\text{5}}{\text{61}}$ minutes past 3 (C) 15$\frac{\text{5}}{\text{60}}$ minutes to 2 (D) 16$\frac{\text{4}}{\text{11}}$ minutes to 4 The right option is A Explaination → Right answer is 16 $\frac{\text{4}}{\text{11}}$ minutes past 3

A clock gains 5 minutes in 24 hours. It was set right at 10 a.m. on Monday. What will be the true time when the clock indicates 10:30 a.m. on the next Sunday? (A) 10 a.m. (B) 11 a.m. (C) 25 minutes past 10 a.m. (D) 5 minutes to 11 a.m. The right option is A Explaination → Right answer is 10 a.m.

A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min 48 sec. fast at 2 p.m. on the following Monday. When was it correct? (A) 2 pm on Tuesday (B) 2 pm on Wednesday (C) 3 pm on Thursday (D) 1 pm on Friday The right option is B Explaination → Right answer is 2 pm on Wednesday

If a clock strikes 12 in 33 seconds, it will strike 6 in how many seconds? (A) $\frac{\text{33}}{\text{2}}$ (B) 15 (C) 12 (D) 22 The right option is B Explaination → Right answer is 15

A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 O’clock, the true time is (a) (b) 59 7 12 minutes past 3 (c) 58 7 11 minutes past 3 (d) 2 3 11 minutes past 4 (A) 4 p.m. (B) 59$\frac{\text{7}}{\text{12}}$ (C) 58$\frac{\text{7}}{\text{11}}$ (D) 2$\frac{\text{3}}{\text{11}}$ The right option is A Explaination → Right answer is 4 p.m.

At what time between 8 and 9 o’clock will the hands of a watch be in straight line but not together? (A) 10$\frac{\text{11}}{\text{10}}$ minutes past 8 (B) 10$\frac{\text{10}}{\text{11}}$ minutes past 8 (C) 11$\frac{\text{10}}{\text{11}}$ minutes past 8 (D) 12$\frac{\text{10}}{\text{11}}$ minutes past 8 The right option is B Explaination → Right answer is 10$\frac{\text{10}}{\text{11}}$ minutes past 8

At what time between 5.30 and 6 will the hands of a clock be at right angles? (A) 43$\frac{\text{5}}{\text{11}}$ minutes past 5 (B) 43$\frac{\text{7}}{\text{11}}$ minutes past 5 (C) 40 minutes past 5 (D) 45 minutes past 5 The right option is B Explaination → Right answer is 43$\frac{\text{7}}{\text{11}}$ minutes past 5

Find the angle between the hour hand and the minute hand o f a clock when the time is 3.25. (A) 43° (B) 37$\frac{\text{1}}{\text{2}}$° (C) 47$\frac{\text{1}}{\text{2}}$° (D) 46° The right option is C Explaination → Right answer is 47$\frac{\text{1}}{\text{2}}$°

How much does a watch gain or lose per day, if it's hands coincide every 64 minutes. (A) 32$\frac{\text{8}}{\text{11}}$ minutes (B) 36$\frac{\text{5}}{\text{11}}$ minutes (C) 90 minutes (D) 96 minutes The right option is A Explaination → Right answer is 32$\frac{\text{8}}{\text{11}}$ minutes

An accurate clock shows 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? (A) 144° (B) 150° (C) 168° (D) 180° The right option is D Explaination → Right answer is 180°

A clock is set right at 5 a.m. The clock loses 16 min. in 24 hours. What will be the true time when the clock indicates 10 p.m. on the 4th day? (A) 11 pm (B) 10 pm (C) 9 pm (D) 8 pm The right option is A Explaination → Right answer is 11 pm

The reflex angle between the hands of a clock at 10:25 is? (A) 180° (B) 192$\frac{\text{1}}{\text{2}}$° (C) 195° (D) 197$\frac{\text{1}}{\text{2}}$° The right option is D Explaination → Right answer is 197$\frac{\text{1}}{\text{2}}$°

At what angle the hands of a clock are inclined at 15 minutes past 5? (A) 72$\frac{\text{1}}{\text{2}}$° (B) 64° (C) 58$\frac{\text{1}}{\text{2}}$° (D) 67$\frac{\text{1}}{\text{2}}$° The right option is D Explaination → Right answer is 67$\frac{\text{1}}{\text{2}}$°

Today is Monday. After 61 days it will be: (A) Wednesday (B) Saturday (C) Tuesday (D) Thursday The right option is B Explaination → Right answer is Saturday 61 ÷ 7 makes remainder 5 By Question today is Monday. So, counting 5 from the next day (i.e. Tuesday), the 61st day felt on Saturday.

What will be the day of the week on 1st January, 2010? (A) Friday (B) Saturday (C) Sunday (D) Monday The right option is A Explaination → Right answer is Friday Here formula is [Date + Month Code + Year(last two digits) + LeapYear Quotient + Century Code] ÷ 7 ie. [1 + 0 + 10 + 2 + 6] ÷ 7 Here remainder is 5 Therefore, the day code of 5 is Friday.

If 09/12/2001 happens to be Sunday, then 09/12/1971 would have been at (A) Tuesday (B) Wednesday (C) Saturday (D) Thursday The right option is D Explaination → Right answer is Thursday Here formula is [Date + Month Code + Year(last two digits) + LeapYear Quotient + Century Code] ÷ 7 For 09/12/2001 [9 + 5 + 1 + 0 + 6] ÷ 7 Since remainder is 0 The given day Sunday falls on date 09/12/2001 is true Similarly, [9 + 5 + 71 + 17 + 0] ÷ 7 Remainder is 4 So, the day falls on 09/12/1971 is Thursday

Find the day of the week on 16th July, 1776 (A) Tuesday (B) Wednesday (C) Monday (D) Thursday The right option is A Explaination → Right answer is Tuesday Here formula is [Date + Month Code + Year(last two digits) + LeapYear Quotient + Century Code] ÷ 7 For 16th July, 1776 [16 + 6 + 76 + 19 + 4] ÷ 7 Since remainder is 2 The day falls on 16th July, 1776 is Tuesday

On January 12, 1980, it was Saturday. The day of the week on January 12, 1979 was – (A) Sunday (B) Saturday (C) Friday (D) Thursday The right option is D Explaination → Right answer is Thursday Here formula is [Date + Month Code + Year(last two digits) + LeapYear Quotient + Century Code] ÷ 7 For January 12, 1980 [12 + 0 + 80 + 20 + 0] ÷ 7 Since remainder is 0 The day falls on date 09/12/2001 is Sunday (not Saturday) Similarly, For January 12, 1979 [12 + 0 + 79 + 15 + 0] ÷ 7 Remainder is 4 So, the day +4 count up from the next day of Sunday falls on Thursday

The calendar for the year 2005 is the same as for the year: (A) 2010 (B) 2011 (C) 2012 (D) 2013 The right option is B Explaination → Right answer is 2011 Since the last two digits divided by 4 makes remainder 1. The same calendar of 2005 can be used again in 2011. ie. 05 ÷ 4 makes remainder 1. So, 6yrs must be added to the given year → 2011 Conditions: If $\frac{\text{Last two digits of the year}}{\text{4}}$ = 0 Given year + 28 must be applied If $\frac{\text{Last two digits of the year}}{\text{4}}$ = 1 Given year + 6 must be applied If $\frac{\text{Last two digits of the year}}{\text{4}}$ = 2 or 3 Given year + 11 must be applied

The year next to 1991 having the same calendar as that of 1990 is- (A) 1998 (B) 2001 (C) 2002 (D) 2003 The right option is C Explaination → Right answer is 2002 Since the last two digits divided by 4 makes remainder 3. The same calendar of 1991 can be used again in 2002. ie. 91 ÷ 4 makes remainder 3. So, 11yrs must be added to the given year → 2012 Conditions: If $\frac{\text{Last two digits of the year}}{\text{4}}$ = 0 Given year + 28 must be applied If $\frac{\text{Last two digits of the year}}{\text{4}}$ = 1 Given year + 6 must be applied If $\frac{\text{Last two digits of the year}}{\text{4}}$ = 2 or 3 Given year + 11 must be applied

Time shown through mirror image is 9:30. So, the true time is:- (A) 2:30 (B) 3:30 (C) 5:30 (D) 8:30 The right option is A Explaination → Right answer is 2:30 Practically, 11:60 - 9:30 = 2:30 Therefore, the real time (true time) is 2:30 Keep in mind that Mirror is placed vertically Whether to find out the True time or the Shown time through mirror... you must subtract the given time from 11:60 If the resultant hour is 12 or more... 12:00 must be subtracted from it If the given time is 6:00 or 12:00, there is no changes in the True time or the Shown time through mirror...

Time shown through mirror image is 12:30. So, the true time is:- (A) 9:30 (B) 10:30 (C) 11:30 (D) 12:30 The right option is C Explaination → Right answer is 11:30 Practically, 11:60 - 12:30 = it is impossible to subtract NOTE: 12:00 can also be express as 0(zero) Therefore, the real time (true time) is 11:60 - 00:30= 11:30 Keep in mind that Mirror is placed vertically Whether to find out the True time or the Shown time through mirror... you must subtract the given time from 11:60 If the resultant hour is 12 or more... 12:00 must be subtracted from it If the given time is 6:00 or 12:00, there is no changes in the True time or the Shown time through mirror...

Time shown through water image is 9:30. So, the true time is:- (A) 10:30 (B) 9:30 (C) 7:30 (D) 8:30 The right option is B Explaination → Right answer is 9:00 Practically, Given time is 9:30 Here the minute 30 in 9:30 is ≤ 30 So, the given time 9:30 must be subtracted from 18:30 and not from 17:90 Therefore, the real time (true time) is 18:30 - 9:30 = 9:00 Keep in mind that Water is always horizontal Whether to find out the True time or the Shown time through water... you must subtract the given time from 18:30 if the subtracted time's minute is ≤ 30. Else the time must be subtracted from 17:90 If the resultant hour is 12 or more... 12:00 must be subtracted from it If the given time is 9:45 or 9:15 or 3:15 or 3:45, there is no changes in the True time or the Shown time through water image...

Time shown through mirror image is 12:40. So, the true time is:- (A) 4:00 (B) 3:30 (C) 2:30 (D) 3:00 The right option is D Explaination → Right answer is 3:00 Practically, Here, the given time is 12:40 where the minute, 40 > 30 in 18:30. Therefore, 18:00 - 12:40 is inappropriate So, 17:90 - 12:40 is to be applied Hence the real time (true time) is 17:90 - 12:40= 15:50 Now, the simple way of knowing the right time is 15:50 - 12:00 = 3:00 o'clock Keep in mind that Water is always horizontal Whether to find out the True time or the Shown time through water... you must subtract the given time from 18:30 if the subtracted time's minute is ≤ 30. Else the time must be subtracted from 17:90 If the resultant hour is 12 or more... 12:00 must be subtracted from it If the given time is 9:45 or 9:15 or 3:15 or 3:45, there is no changes in the True time or the Shown time through water image...