Question

A clock loses 3% time during the first week and then gains 2% time during the next one week. If the clock was set right at 12 noon on a Sunday, what will be the time that the clock will show exactly 14 days from the time it was set right ?

• A. $1:36:48$
• B. $1:40:48$
• C. $1:41:24$
• D. $10:19:12$

Answer 1

The correct option is D $10:19:12$

The clock loses 3% time during the first week.
In a day there are 24 hours and in a week there are 7 days.
Therefore, there are $7\times 24=168$ hours in a week.
If the clock loses 3% time during the first week, then it will show a time which is 3% of 168 hours less than 12 Noon at the end of the first week = 5.04 hours less.
Subsequently, the clock gains 2% during the next week.
The second week has 168 hours and the clock gains 2% time = 2% of 168 hours = 3.36 hours more than the actual time.
As it lost 5.04 hours during the first week and then gained 3.36 hours during the next week, the net result will be a $-5.04+3.36=-1.68$ hour net gain in time.
So the clock will show a time which is 1.68 hours less than 12 Noon two weeks from the time it was set right. 1.68 hours = 1 hour and 40.8 minutes = $12-(1hour+40minutes+48seconds)$. i.e. $10:19:12$