Question

A clock is set right at $\text{2 p.m.}$ If it gains one minute an hour, what is the true time when the clock indicates $7$ pm the same day _______________.

• A. $55\frac{5}{61}\text{minutes past 6 pm}$
• B. $53\frac{5}{61}\text{minutes past 8 pm}$
• C. $52\frac{5}{61}\text{minutes past 4 pm}$
• D. $57\frac{5}{61}\text{minutes past 5 pm}$

Answer 1

The correct option is A $55\frac{5}{61}\text{minutes past 6 pm}$

⇒⇒ Time interval indicated by incorrect clock
=7pm−2pm=5=7pm−2pm=5 hours
Houes gained by incorrect clock in one hour
=+1minute=+160=+1minute=+160 hour
Using formula
True time intervalTime interval in incorrect clockTrue time intervalTime interval in incorrect clock
=11+hour gained in 1 hour by incorrect clock=11+hour gained in 1 hour by incorrect clock
True time interval5=11+160True time interval5=11+160
True time interval=5×6061=45661hoursTrue time interval=5×6061=45661hours
True time=2pm+45661hoursTrue time=2pm+45661hours
=6pm and5661×60minutes=6pm and5661×60minutes
=55561minutes past 6 pm