Learn and practice Problems on clocks with easy explaination and shortcut tricks. All questions and answers on clocks covered for various Competitive Exams

Solve Problems on clocks:

1) How many times the hands of a clock coincide in a day?

At 3 O’ clock, the hands of the clock are 15 minute spaces apart. To be in straight line and in opposite directions, the hands must be 30 minutes spaces apart.

Now, the minute hand is 15 minute spaces behind the hour hand, so it has to gain 45 (15+30) minute spaces over the hour hand.

55 minute spaces are gained in 60 minutes by the minute hand

45 minutes will be gained in =* 45 minutes

=540/11

= 49 1/11 minutes past 3.

3) An accurate clock indicates 8 O’ clock in the morning. Through how many degrees the hour hand turns when the clock indicates 3 O’ clock in the afternoon?

As we know, the hands of a clock will be at 90° between H: 30 and (H+1) O’clock at (5H + 15) 12/11 minutes past H O’ clock.

∴ Required time = (5H + 15) 720/11

Now, H = 4

= (5*4 + 15) 720/11 = 20 + 15 * 720/11

=35 * 12/11

=420/11

=38 2/11 minutes past 4

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9) A watch which gains uniformly is 5 minutes slow at 6am on Monday and is 5 minutes 48 seconds fast at 6pm on the following Monday. When was it correct?

Between 5 O’ clock and 6 O’ clock, the hands will be 10 minutes spaces apart twice, i.e. when the minute hand is 10 minute spaces behind the hour hand and when the minute hand is 10 minute space ahead of the hour hand.

Case 1: When the minute hand is 10 minutes spaces behind the hour hand;

At 5 O’ clock, the minute hand is 25 minute spaces behind the hour hand.

So, the minute hand has to gain (25-10) = 15 minute spaces over hour hand to be 10 minute spaces apart.

Now, 55 minute spaces are gained in 60 minutes.

15 minute spaces will be gained in * 15 = 16 4/11 minutes

∴The hands of the clock will be 10 minute spaces apart at 16 4/11 minutes past 5.

Case 2: When the minute hand is 10 minute spaces ahead of the hour hand.

The minute hand has to gain (25 + 10) = 35 minute spaces over the hour hand.

Now, 55 minutes are gained in 60 minutes.

35 minutes will be gained in * 35 = 38 2/11 minutes

∴ The hands of the clock will be 10 minute spaces apart at 38 2/11minutes past 5.