GATE CE 2018 Set 2 — Question 7
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Question
A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 AM on 11th July. What will be the correct time to the nearest minute when the clock shows 2 PM on 15th July of the same year?
Correct answer
(B) 12:58 PM
Solution
A faulty clock gains 15 minutes in 24 hours.
This means 24 hours and 15 minutes on the faulty clock corresponds to 24 hours on a correct clock.
Faulty time interval = hours.
Correct time interval = 24 hours.
Ratio of correct time to faulty time = .Time elapsed on the faulty clock from 9 AM 11th July to 2 PM 15th July:
From 11th 9 AM to 15th 9 AM = 4 days = 96 hours.
From 15th 9 AM to 15th 2 PM = 5 hours.
Total faulty time elapsed = hours.Actual time elapsed = hours.
hours = 4 days and hours.
minutes.
So, the correct time is 4 days, 3 hours, and 58 minutes (to the nearest minute) from 9 AM 11th July.
9 AM + 3 hours 58 minutes = 12:58 PM on 15th July.
This means 24 hours and 15 minutes on the faulty clock corresponds to 24 hours on a correct clock.
Faulty time interval = hours.
Correct time interval = 24 hours.
Ratio of correct time to faulty time = .Time elapsed on the faulty clock from 9 AM 11th July to 2 PM 15th July:
From 11th 9 AM to 15th 9 AM = 4 days = 96 hours.
From 15th 9 AM to 15th 2 PM = 5 hours.
Total faulty time elapsed = hours.Actual time elapsed = hours.
hours = 4 days and hours.
minutes.
So, the correct time is 4 days, 3 hours, and 58 minutes (to the nearest minute) from 9 AM 11th July.
9 AM + 3 hours 58 minutes = 12:58 PM on 15th July.
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