Question

How many times in a day the hands of a clock are straight?

Answer 1

Calculate the number of times the hands of a clock are straight:

For the hands of a clock to be considered straight, they must either coincide or be opposite to each other.

Times when the arms coincide: $12:00,1:05,2:10,3:15,4:20,......,10:55=11$times in $12$ hours

Hence the arms coincide with each other $22$ times in a day

Times when the arms are exactly opposite: $12:30,1:35,2:40,3:45,.......,11:25=11$times in $12$ hours

So, the arms are opposite to each other $22$ times in a day

Therefore, the arms are straight for $22+22=44$ times in a day