At 12:45, the minute hand is on the 9 ( 90° between 9 and 12) and the hour hand is 3/4 of the way between 12 and 1
so the degree value from 12 to 1 is:. There are 30° between numbers, so it is=(3/4*30)= 22½° past 12
Every minute, the minute hand goes 6° while the hour hand goes ½° so it is gaining on it by 5½° per minute.
so after 15 minute the minute + (3/4) of 5 minute it will coincide with hour hand travelling a degree of 112½°
It has to make up 112½° so dividing by 5½°/minute we have:
112.5 / 5.5
= 20.45
Adding to 12:45, we get a time between 1:05 and 1:06.
Answer:
c) 1:05 pm and 1:06 pm