Test Level 2: Clocks & Calendars - 1 - CAT MCQ

At 5 o'clock, the hands are 25 minute space apart.
To be at right angle, that too between 5:30 and 6:00, the minute hand has to gain (25 + 15) or 40 minute space.
55 minute space is gained in 60 minutes.
40 minute space is gained in 40 ×
Therefore, required time =  

The hands will coincide once every hour, except from 11 to 1, when the hands coincide once in two hours at 12. Thus, the hands coincide 11 times in 12 hours or 22 times in 24 hours.

From Saturday noon to the following Monday till 3 p.m, total time = 51 hours
Now, minutes are gained in 51 hours.
1 minute shall be gained in 51 × (5/34) hours.
Thus, 2 minutes shall be gained in (2 × 51) × (5/34) hours = 15 hours after 12:00 p.m. Saturday, i.e. 3:00 a.m. Sunday.

Every leap year repeats its calendar after 28 years.
Since year 1988 was a leap year, the calendar of year 2016 will be the same as that of year 1988.

1988 April 4th to 1987 November 3rd, we have 27 + 31 + 31 + 29 + 31 + 4 = 153 Days = 21 weeks + 6 odd days.
Six days before(because later date is given and former date is asked) a Monday comes a Tuesday.

Year 2002, after 14 odd days, has the same calendar as 1991.

As the given year is a leap year, so 1st August in the next year will be Tuesday. After 2 years, it will be Wednesday.
After 3 years, it will be Thursday.

Number of days = 30 (January) + 28 (February) + 15 (March) = 73

From 8 a.m. today to 1 p.m. the following day, there are a total of 29 hours. Also, our clock is gaining 10 minutes in 24 hours.
∴ In a day, 1450 (24 × 60 + 10) minutes of our clock means 1440 (24 × 60) minutes of true time.
1 minute of our clock means 1440/1450 minutes of true time.
(29 × 60) minutes of our clock = 1440/1450  × 29 × 60 minutes of true time
= 28.8 × 60 minutes of true time
= 28 hours 48 minutes of true time
Thus, the true time will be 48 minutes past 12.

Hands of the clock are straight when they are coinciding and when they are pointing towards each other (30 min spaces apart). Hands will coincide once every hour except from 11 to 1 where hands are coinciding once in two hours at 12. Thus, hands will coincide 11 times in 12 hours or 22 times in 24 hours.