KVPY SA Exam 2011 Question Paper

Question : 14 of 80

Marks: +1, -0

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?

$1/2$
$5/8$
$3/4$
$5/6$

Validate

Solution:

The clock will show the incorrect time (between 1 – 2, 10 - 11, 11 - 12, 12 - 1 day and night both)
∴ in correct time 8 × 60 = 480 (each minute it will display 1)
Remaining 20 hours it will show the incorrect time 16 × 15 = 240
Total incorrect time = 240 + 480 = 720
correct time = 1 – incorrect time

=1-720/{24×60}=1/2

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