A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock indicates 1 p.m. on the following day?

Explanation

From 8 am to 8 am next day, the clock will show 8:10 am. 24 hr = (24 × 60) minutes Real time of (24 × 60 + 10) minute = (24 × 60) minutes Real time of 1450 minutes = 1440 minutes Real time of (24 × 60 + 5 × 60) minutes = ($\frac{1440}{1450} \times 1740$) minutes [∵ Total time from 8 am to 1 pm the next day. = (24 × 60) min. + (5 × 60) min.= 1740] = $\frac{144}{145} \times 1740$ = 144 × 12 = 1728 min. = 28 hr. + 48 min. = 24 hr. + 4 hr. + 48 min. So, on next day, at 1 o’clock in the afternoon, when the clock shows the hand, actual time will be. = 8 am + (4 hr + 48 min) = 12 : 48 pm ∴ According to question, clock gained 8 min time interval in 48 hours ∴ The time interval per minutes is achieved in 6 hours. The clock was 3 minutes behind, hence just after completing 3 minutes time duration, clock will show right time. Time taken by the clock in 3-minutes interval = 3 × 6 =18 hours ∴ 2 pm (Monday) + 18hr = 6 am (Tuesday)