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A certain 12 -hour digital clock displays the hour and the minute of a day. Due to a defect in the clock whenever the digit 1 is supposed to be displayed it displays 7 . What fraction of the day will the clock show the correct time?
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Verified Answer
The correct answer is:
$\frac{1}{2}$
The clock will show the incorrect time (between $1-2,10-11,11-12,12-1$ day and night both)
$\therefore$ in correct time $8 \times 60=480$ (each minute it will display 1 )
Remaining 20 hours it will show the incorrect time $16 \times 15=240$
Total incorrect time $=240+480=720$
correct time $=1-$ incorrect time
$=1-\frac{720}{24 \times 60}=1 / 2$
$\therefore$ in correct time $8 \times 60=480$ (each minute it will display 1 )
Remaining 20 hours it will show the incorrect time $16 \times 15=240$
Total incorrect time $=240+480=720$
correct time $=1-$ incorrect time
$=1-\frac{720}{24 \times 60}=1 / 2$
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