A clock is such that it loses 4 minutes each day. The clock is set right on February 25, 2008 at 2 p.m. How many minutes should be added to get the right time when the clock shows 9 am on 3rd March, 2008?
Solution
✅ Correct Option: 1
Actual time passed $=(6$ days $\times$ $24 $ hours $)+19$ hours $=163$ hours. Given that the clock loses $4$ minute in every single day. $1$ day $=24$ hours $=24 \times 60=1440$ minutes. In $1440$ minutes, the clock losses $4$ minutes. Therefore, the minute hand moves at a slightly slower pace. The speed of minute hand can be expressed as $\frac{1436}{1440}$ fractional part of one minute. Actual time elapsed is just the reciprocal of it, i.e $=\frac{1440}{1436}$ Thus in the given time of $163$ hours, Actual time elapsed $=163$ (hours) $\times$ $60$ (minutes) $\times$ $\frac{1440}{1436}$ (minutes hand) But due to loss in time, the time elapsed by clock is $=163 \times 60$ Difference $=\left(163 \times 60 \times\left(\frac{1440}{1436}\right)\right)-(163 \times 60)$ $=\frac{14083200}{1436}-9780=\frac{9780}{359}$ This difference must be added to get the right time.