Puzzles

75 degrees is the angle between the minute hand and the hour hand of a clock when the time is 8:30.

Explanation:

Formula

A = 30H – (11/2) M

• A is the Required Angle
• H is the position of the Hour hand
• M is the minutes

A = 30 x 8 – (11/2) x 30

A = 240 – 165

A = 75

Hence, the two hands of a clock will be inclined at an angle of 75 degrees when the time is 8 hours 30 minutes.

The minute hand in a clock moves around 24 times in a day.

The hour hand in a clock moves around 2 times in a day i.e., it completes one rotation every 12 hours.

In 12 hours, the hour hand makes one rotation, and the minute hand makes 12 rotations. So the minute hand passes (coincides with) the hour hand 11 times in 12 hours or 22 times in 24 hours.

The clock ticks six o’clock in 26 minutes.

Explanation:

As per the given data, the clock has already ticked 3 o’clock. So, let’s consider there are “M” minutes until it’s six o’clock in that clock.

When you observe, there are 180 minutes between 3 o’clock and 6 o’clock. So, it is clear that 180 – M is the number of minutes past 3 o’clock. And also, according to the question, 50 minutes ago it was four times the minutes past 3 o’clock.

So, we need to consider 180 – 50 = 130 minutes instead of 180 minutes as it was already past 50 minutes.

Now, the required minutes is 4 times. So, it will be 4 x M.

==> 4M = 130 – M

==> 4M + M = 130

==> 5M = 130

==> M = 26

Hence, 26 minutes are left until the clock ticks six o’clock