Question

A 12 dial clock has its minute hand defective. Whenever it touches dial 12, it immediately falls down to 6 instead of running smoothly (the hour hand remains unaffected during that fall). It was set right at 12 '0' clock in the noon. How many times the two hands of a watch form right angle from 12 O' clock noon to 6 O'clock evening.

• A. 6
• B. 10
• C. 11
• D. 12

Answer 1

The correct option is D 12

The answer is option D

Between 12 O'clock noon to 6 pm, there are 6 hours

In every hour, the clock has the chance to be at ${90}^o$ twice, but due to the defect, the minute moves to 6 at the stroke of every hour.

In the first 30 mins, the minute hand makes ${90}^o$ with the hour hand once.

After 30 mins, the minute hand again moves to 6. In the next 30 mins, it again makes ${90}^o$ with the hour hand. Like this, there would be 2 times in an hour when the minute hand makes 90^o with the hour hand

So on, till 6 pm, there would be 12 times when the minute and hour hand will be perpendicular to each other