Test Level 2: Clocks & Calendars - 2 - CAT MCQ

In this type of problem, the formula is"

Here, H is replaced by the first interval of given time and t is spaces apart.
Given that H is 5.

 mins or 24 mins
Therefore, the hands will by 3 minutes apart at 336/11 minutes or 24 minutes past 5.

Since February had 5 Sundays in 1648, so February 1, 1648 was a Sunday.
So, number of odd days up to February 1, 1748 = 5
Number of odd days up to February 1, 1750 = (2 + 1) = 3
Number of odd days up to February 13, 1750 = 12
So, total number of odd days = 5 + 3 + 12 = 20
So, number of odd days from February 1, 1648 to February 13, 1750 = 6
Hence, the answer is 'Saturday'.

Using formula, [where θ = angle between the hour-hand and the minute-hand, m - minutes, h - hours]

There will be 2 values.
 minutes past 4 or m = minutes past 4.

Hour hand rotates 360° in 12 hrs, so it rotates 30° in 1 hour.
So, in 1 min, it rotates 0.5°.
Minute hand rotates 6° in 1 min.
So, angle at 8:45 = 0.25 × 30° = 7.5°
At 4:15, angle will be 0.25 × 30° + 30° = 7.5° + 30° = 37.5°
So, 37.5° + 0.5t + 7.5° = 6t
45 = 5.5t

Hence clock makes same angle at 23minutes past 4 o'clock

Time from 3 pm on a day to 6 am after 4 days is 87 hours. Now, 23 hr 51 min on this clock are the same as 24 hr on the correct clock.
That is, on this clock = 24 hr on the correct clock
∴ 87 hr on this clock = hr on the correct clock
= 87 hr and 33 minutes approx. on the correct clock
So, the correct time will be 6:33 am.

Number of days from March 15th, 2013 to July 10th, 2013 = 16 + 30 + 31 + 30 + 10 = 117
On dividing 117 by 7, remainder is 5.
Now, counting 5 days after Friday, we get Wednesday.

Using formula: 

As 2012 was a leap year, so the number of days in each month from 23rd January, 2011 to 31st July, 2013 is given as follows.
Since 2011 is not a leap year = 365 - 22 = 343 days
Number of days in 2012 = 366 days (leap year)
Number of days in 2013:
January = 31 days
February = 28 days
March = 31 days
April = 30 days
May = 31 days
June = 30 days
July = 31 days
Total number of days in 2013 = 212
Therefore, total number of days from 23rd January, 2011 to 31st July, 2013 = 343 + 366 + 212 = 921

The time duration from 10 a.m. on Friday to 2 p.m. on the following Monday is 76 hours.
The clock gains 1 minute per hour.
∴ Time gained in 76 hours = 76 minutes = 1 hour 16 minutes
∴ Time shown by the second clock will be 3:16 p.m.

He returned after 8 o'clock but before 9 o'clock, at such a time when both the minute hand and the hour hand were found to be coinciding.
In a simple way, we need to calculate the time when the angle between the minute hand and the hour hand is zero.
Angle between the minute hand and the hour hand at 8 o'clock = 8 × 30 = 240°
We can reduce the difference of 5.5 degree in 1 min,
Required time = 8 hrs + 240 × 2 ÷ 11

In 1 hour, the first clock turns 62 minutes and the second 56 minutes. This implies that for every 56 minutes of the second clock, the first clock gains 6 minutes.
'The second clock shows 10 p.m.' means that it runs for 14 hours.
In this time, the first clock gains = 90 minutes.
So, the time will be 11:30 p.m.

To be together between 9 and 10 o'clock, the minute hand has to gain 45 minute spaces.
55 minute space is gained in 60 minutes.
45 minute space will be gained in 
At 49minutes past 9, the hands of the clock will be together.

15th August, 1987 means '1986 years + 7 months + 15 days'.
1600 years have 0 odd days, and 300 years have 1 odd day.
86 years contain 21 leap years and 65 ordinary years and therefore, 42 + 65 = 107 or 2 odd days.
1986 years give 0 + 1 + 2 = 3 odd days
Number of days from 1st January, 1987 to 15th August, 1987 = 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15
= 227, i.e. 3 odd days
Total number of odd days = 3 + 3 = 6
The day on 15th August, 1987 was a Saturday.

Note that at 1:00, the minute hand and hour hand are 5 minutes apart from each other. Then, between 1:00 and 2:00, only once, i.e. some time after 1:10, minute hand and hour hand will be 6 minutes apart from each other. Similarly, at 11:00, the minute hand and hour hand are 5 minutes apart from each other. Then, between 11:00 and 12:00, only once, i.e. some time before 11:50, minute hand and hour hand will be 6 minutes apart from each other. It can be observed twice that the hour hand and minute hand are 6 minutes apart from each other. Therefore, the answer is 44 times.

The watch loses 5 minutes in 3 hours.
It loses 1 minute in (3/5) hours.
To show the correct time again, watch must create a 24-hour difference. (Since in one round, an hour-hand covers 24 hours.)
So, it loses 60 minutes in (3/5) × 60 hours or 36 hours.
It loses 24 hours in 36 × 24 hours or 864 hours or 36 days
Therefore, after exactly 36 days, the clock will show the correct time.

We know that the clock gains 2 minutes every hour.
Number of hours between 6 am and 9 pm = Number of hours between 6 am and 12 noon + Number of hours between 12 noon and 9 pm
= 6 + 9 = 15 hours
Hence, in 15 hours, the clock will gain 15 x 2 = 30 minutes

He teaches for 8 consecutive days and takes an off on the 9th day.
For each off day, 8 teaching days + 1 off day = 9 days passed
So, on the 12th off day, there are 9 x 12 = 108 days passed
We have to find the day of the week on 12th off day.
So, we have to deduct a day.
Number of odd days = (108 - 1)/7 = 107/7 = 2
He started teaching on Monday.
So, the 12th off day is Monday + 2 = Wednesday

Every hour:

1. Table clock - Wall clock = +10 minutes ⇒ 1 hour in 6 hours
2. Alarm clock - Table clock = -5 minutes ⇒ 30 minutes in 6 hours
3. Wrist watch - Alarm clock = +5 minutes ⇒ 30 minutes in 6 hours

Also, every hour, wall clock loses 10 minutes.
If it is 6 hours since 12 noon, then time shown by the wall clock = 6:00 - 1 hour = 5:00 pm
⇒ Time shown by table clock with reference to wall clock = 5:00 + 50 min = 5:50 pm
⇒ Time shown by alarm clock with reference to table clock = 5:50 pm - 25 minutes - 25/6 minutes = 5:21 pm
⇒ Time shown by wrist watch = 5:21 + 25 minutes + 21/6 = 5.47 pm
Hence, 5.47 pm is the answer.

Today is Friday.
Lets solve this problem in reverse order.
Then, we have day after tomorrow = Sunday
The day before the day after tomorrow = Saturday
Three days after the day which is before the day after tomorrow = Tuesday
Hence, Tuesday is the correct answer.

Now, the angle is 
If the angle between the hands is 70°, then the time can be found as follows.

M = 220/11 = 20 minutes or M = 
So, the same angle will be made at 6:45
So, the required answer is 6:45- 6:20 = 25minutes