Table of contents  
Points to Remember  
Solved Problems 
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Example 1: At what time between 4 and 5, the minute hand will be 2 minutes spaces ahead of the hour hand?
At 4 O'clock, the two hands are 20 min spaces apart.
In this case, the min hand will have to gain (20 + 2) i.e. 22 – minute spaces.
So, 22 – minute spaces will be gained in (60/55) × 22 = 24 min.
Example 2: The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much does the clock lose or gain in 12 hours?
In a correct clock, the minute hand and hour hand should meet after every 65 5/11 min.
But we know that they are meeting after every 65 minutes.
So, the gain in 65 minutes is 5/11 minutes.
Gain in 12 hours = (120 × 60/65) × (5/11) = 720/143 = 5 5/143 min.
Example 3: A clock is set right at 10 am. The clock gains 5 minutes in 12 hours. What will be the true time when the clock indicates 3 pm on the next day?
Time from 10 am to 3 pm on the following day is 29 hrs.
Now, 12 hrs 5 min i.e. 145/12 hrs of this clock = 12 hours of correct clock.
So, 29 hours of this clock is (29 × 12 × 12)/145 = 144/5 = 28 hours 48 minutes.
So, the time is 12 minutes before 3 pm.
Example 4: The minute hand of a clock overtakes the hour band at interval of 60 mins. How much a day does the clock gain or lose?
In a correct clock, minute hand gains 55 minute spaces over the hour hand in 60 minutes.
Therefore, 60 min spaces are gained in (60 × 60)/55 = 720/11 minutes.
In other words, minute hand overtakes hour hand in every 720/11 minutes.
In the example given, minute hand overtakes hour band in 60 minutes.
Therefore, gain in 60 minute = (720/11)  60 = 60/11 minutes.
Gain in 24 hours = (60/11) × 24 = 1440/11 min
gain/loss =
Since the sign is +ve, clock gains 1440/11 min in a day.
Example 5: The minute hand of a clock overtakes the hour band at an interval of 66 mins. How much a day does the clock gain or lose?
As we have seen previously, minute hand overtakes hour hand in every 720/11 minute.
In this example, minute hand overtakes hour band in 66 minutes
Therefore, loss in 66 minute = 66  720/11 = 6/11 minutes
Loss in 24 hours = 6/11 × 1/66 × 66 × 24 = 1440/121 min
gain/loss
Since the sign is ve, the clock loses 1440/121 min a day.
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