Worksheet Solutions: Clocks | Know Your Aptitude Class 3 To 5 - Class 5 PDF Download

Section A: True or False

Q1: The angle between the hour hand and the minute hand of a clock is always 90 degrees at 3:15.

Ans: False
Explanation: At 3:15, the minute hand will be on the 3 and the hour hand will be slightly past the 3. The angle between the hands will be less than 90 degrees.

Q2: The angle between the hour hand and the minute hand of a clock is 180 degrees at 6:00.

Ans: True
Explanation: At 6:00, the minute hand will be on the 12 and the hour hand will be on the 6. The angle between the hands will be 180 degrees.

Q3: The angle between the hour hand and the minute hand of a clock is 0 degrees at 12:30.

Ans: True
Explanation: At 12:30, the minute hand will be on the 6 and the hour hand will be on the 12. The angle between the hands will be 0 degrees.

Q4: The angle between the hour hand and the minute hand of a clock is always 180 degrees at 9:45.

Ans: False
Explanation: At 9:45, the minute hand will be on the 9 and the hour hand will be between the 9 and the 10. The angle between the hands will be less than 180 degrees.

Q5: The angle between the hour hand and the minute hand of a clock is always 90 degrees at 12:15.

Ans: True
Explanation: At 12:15, the minute hand will be on the 3 and the hour hand will be on the 12. The angle between the hands will be 90 degrees.

Section B: Fill in the Blanks

Q1: An accurate clock shows 10 o'clock. In how many minutes will the minute hand gain 60 degrees on the hour hand?

Ans: 120 minutes
Explanation: The minute hand moves 6 degrees per minute, while the hour hand moves 0.5 degrees per minute. To gain 60 degrees, the minute hand needs to catch up with the hour hand by 60 degrees / (6 degrees/minute - 0.5 degrees/minute) = 120 minutes.

Q2: At what time between 3 PM and 4 PM will the hands of a clock be coincident?

Ans: 3:27 PM
Explanation: To find the coincident time, we need to solve the equation: 30h - 11/2m = 0, where h is the hour and m is the minute. Substituting the values, we get 30(3) - 11/2(m) = 0. Solving for m, we find m = 27. Therefore, the hands of the clock will be coincident at 3:27 PM.