Question

A clock is set right at 1 p.m if it gains one minute in an hour then what is the true time when the clock indicates 6 p.m the same day?

Answer 1

Time interval indicated by incorrect clock

= 6 p.m.-1 p.m. = 5 hours

Time gained by incorrect clock in one hour

= + 1 minute = + $\frac{1}{60}$ hour

Using the formula,

$\frac{Truetimeinterval}{Timeintervalinincorrectclock}$

=$\frac{1}{1+hourgainedin1hourbyincorrectclock}$

$\Rightarrow \frac{Truetimeinterval}{5}=\frac{1}{1+\frac{1}{60}}$

$\Rightarrow Truetimeinterval=\frac{5\times 60}{61}=4\frac{56}{61}$

$\therefore$ True time = 1 p.m. + $4\frac{56}{61}hrs.$

= 5 p.m. + $\frac{56}{61}$ hrs. = 5 p.m. + $\frac{56}{61}$ $\times 60$ min

= $55\frac{5}{61}$ minutes past 5