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Clocks - Quant/Math - CAT 2016

Question 4 the day: June 20, 2003

The CAT Practice question for the day is from the topic Clocks.

Question:
A clock loses 1% 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?
(1) 1: 36: 48
(2) 1: 40: 48
(3) 1: 41: 24
(4) 10: 19: 12
Correct choice (2). Correct Answer - 1: 40: 48

Solution:

The clock loses 1% time during the first week.

In a day there are 24 hours and in a week there are 7 days. Therefore, there are 7 * 24 = 168 hours in a week.

If the clock loses 1% time during the first week, then it will show a time which is 1% of 168 hours less than 12 Noon at the end of the first week = 1.68 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 1.68 hours during the first week and then gained 3.36 hours during the next week, the net result will be a -1.68 + 3.36 = 1.68 hour net gain in time.

So the clock will show a time which is 1.68 hours more than 12 Noon two weeks from the time it was set right.

1.68 hours = 1 hour and 40.8 minutes = 1 hour + 40 minutes + 48 seconds.

i.e. 1 : 40 : 48 P.M.