A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at 9 {AM} on 11^{\text{th }} July. What will be the correct time to the nearest minute when the clock show 2 PM on 15^{\text{th }} July of the same year?

GATE Civil Engineering (CE) 2018 Shift 2 Solved Paper

Question : 6 of 65

Marks: +1, -0

A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the correct time at

9 {AM}

11^{\;\text "th "\;}

July. What will be the correct time to the nearest minute when the clock show 2 PM on

15^{\;\text "th "\;}

July of the same year?

Solution:

9 AM of 11 July of 2 PM on

15^{\;\text "th "\;}

July

=101

hours

(24+\;{15}/{60})

hours of incorrect clock

=24

hours of correct clock

(24+\;{15}/{60})

hours of IC

=24

hours of correct clock
1 hour of IC

=\;{96}/{97}

hours of correct clock
101 hour of IC

=\;{96}/{97} × 101

hours of correct clock

=99.958

hours of correct clock

=99

hours

+0.95876 × 60

minutes of correct clock

=99

hours

+57.525

minutes

=99

hours and approx. 58 minutes
So, correct time will be

2 {PM}, 11^{\;\text "th "\;}

July

+(99

hours and 58 minutes

)=12: 58 {PM}

15^{\;\text "th "\;}

July

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