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?

12 : 45 PM

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12 : 58 PM

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1 : 00 PM

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2 : 00 PM

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Solution

The correct option is B 12 : 58 PM
9 Am of 11 July of 2 PM on 15th July = 101 hours

$(24 + \frac{15}{60}) h o u r s o f i n c o r r e c t c l o c k = 24 h o u r s o f c o r r e c t c l o c k$

$(24 + \frac{15}{60}) h o u r s o f I C = 24 h o u r s o f c o r r e c t c l o c k$

$1 h o u r o f I C = \frac{96}{97} h o u r s o f c o r r e c t c l o c k$

$101 h o u r o f I C = \frac{96}{97} \times 101 h o u r s o f c o r r e c t c l o c k$

$= 99.958 h o u r s o f c o r r e c t c l o c k$
$= 99 h o u r s + 0.95876 \times 60 m i n u t e s o f c o r r e c t c l o c k$

$= 99 h o u r s + 57.525 m i n u t e s$

$= 99 h o u r s a n d a p p r o x 58 m i n u t e s$

So correct time will be

2 PM, 11th July + (99 hours and 58 minutes)

= 12 : 58 PM on 15th July

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