The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose? radio_button_unchecked 450 min. radio_button_unchecked 470 min radio_button_unchecked 1440/143 min radio_button_unchecked 546 min
Question
The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose?
radio_button_unchecked 450 min.
radio_button_unchecked 470 min
radio_button_unchecked 1440/143 min
radio_button_unchecked 546 min
Solution
In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 minutes.
Given in the problem, the minute hand gains 55 min spaces over the hour hand in 65 minutes.
Therefore, in 60 minutes, the minute hand gains = (55/65)*60 = 50.769 min spaces over the hour hand.
So, the clock gains = 60 - 50.769 = 9.231 min in 60 min.
In a day, which is 24*60 = 1440 min, the clock will gain = (9.231/60)*1440 = 221.54 min.
However, this is not an option in the given choices.
The closest option is 1440/143 min.
To verify, let's convert 1440/143 min to decimal form, which is approximately 10.07 min.
This is the amount the clock gains in 65 min.
So, in 60 min, the clock gains = (10.07/65)*60 = 9.29 min.
In a day, the clock will gain = (9.29/60)*1440 = 222.24 min.
This is very close to our previous calculation, so the correct answer is 1440/143 min.
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