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12 votes

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

- $12:45$ PM
- $12:58$ PM
- $1:00$ PM
- $2:00$ PM

13 votes

Best answer

the clock will gain 1 h in four days.

So, when the correct time on 15 July is $9$ $AM$, the clock will show $10$ $AM$.

Now, since the clock gains $15$ minutes in $24$ hours, it will gain nearly $\frac{15}{24}\times 4 = 2.5$ minutes in $4$ hours.

So, when clock shows 2 PM on 15 July, then actual time is nearly $1$ hour $2.5$ minutes behind it. i.e., around $12:58$ $PM$

Correct Answer: $B$

2 votes

$11^{th} july=9 AM$

A faulty wall clock is known to gain 15 minutes every 24 hours.

$11^{th}-12^{th} july=9:15 AM$

$12^{th}-13{th} july=9:30 AM$

$13^{th}-14^{th} july=9:45 AM$

$14^{th}-15^{th} july=10:00 AM(actual\ time=9:00AM)$

$24H\Rightarrow 15min(gain)$

$4H\Rightarrow ?min$

$?=2.5min(gain)$

the correct time to the nearest minute when the clock shows 2 PM on 15th July

$Correct\ time\ will\ be\ 1hour\ 2.5min\ behind\ from\ 2PM\approx12:58PM$