MindTree Clocks and Calendars Quiz 1

Formula used= θ=(11/2)M -30H where, H= hours, M= minutes
H= 5 , M= 40
Required angle, θ=(11/2)40 -30×5 = 70°

At 5 O’ clock, the two hands are 25 min spaces apart.
In this case, the min hand will have to gain (25 + 8) i.e. 33 – minute spaces.
So, 33 – minute spaces will be gained in (60/55)×33=36 min.
The hands will be 8 min apart at 36 min past 5

In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min.
To be together again, the minute hand must gain 60 min over the hour hand.
We know that 60 min are gained in (60/55)×60 = 65(5/11)min
But they are together after 63 min. gain in 63 min = 65 – 63 = 2 = 65(5/11) - 63=2(5/11) = (27/11)min.
Gain in 24 hrs = = 27×60×24/11×63 = 56(8/77)min.

The clock has totally gained 16 minutes and 40 sec. i.e. 1000 seconds in 160 hrs.
In order to show the right time, the clock has to gain only 6 min i.e. 360 seconds.

Just apply the chain rule,
the clock gained 1000 sec in 160 hrs.
It will gain 360 sec. in 360 × 160/1000 = 288/5 hrs i.e. 57 3/5.
Adding 57 hrs & 36 minutes in Monday 5 p.m. we get-
2:36 a.m. on Thursday.

8: 30. Angle between 6 and 8 hour spaces is 30 × 2 = 60°. For additional 30 min, angle = 30 = 15°. Hence, required angle = 60 + 15 = 75°

In a span of 12 hrs, the hands of a clock are at right angles exactly 22 times.

So, in a span of 24 hrs, they are at right angles exactly 44 times.

In a span of 24 hours, the hands of a clock are in opposite directions exactly 22 times
& hands of a clock coincide exactly 22 times in a span of 24 hours.
Therefore, they are straight (22 + 22) i.e. 44 times in a span of 24 hours

Between 7 and 8, the hands will be in opposite directions at (5×7 – 30)×(12/11) = 60/11 min.

i.e. 5(5/11) min past 7.

Required angle will be 30×4 = 120°, because between 12 and 4 there are 4 hours and each hour = 30°

From 10 am on 1st day to 4 am on 5th day is total 114 hours.
When a clock loses 15 min, then 23 hours 45 min of this clock are the same as 24 hours of correct clock
i.e. 95/4 hours of this clock = 24 hours of correct clock.
95/4 hours of this clock =((24×4/95)×114) hours of correct clock
= 115.2 hours of correct clock which is equal to 115 hours 11 min.
The correct time is 5:11 am.