Question

A certain $12$-hour digital clock displays the hour and 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?

• A. $\frac{1}{2}$
• B. $\frac{5}{8}$
• C. $\frac{3}{4}$
• D. $\frac{5}{6}$

Answer 1

The correct option is B $\frac{5}{8}$

The clock will show 1 in an hour for 19 time for 11 hours it will show the incorrect time for $(19\times 11)$ time. The last 12th hour will always show the in correct time so total in correct time.
$(19\times 11+60)$ min = $269$ min
there are $24$ hours in a day to $=269\times 2=538$ min
$538$ min = $\frac{269}{30}=9$ hours
the fraction day when the clock shows the correct time is $=1-\frac{9}{24}$
$=1-\frac{3}{8}=\frac{5}{8}$