GATE Civil 2018 Set 2 | GA | Question: 7

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 $11$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?

• A. $12:45$ PM
• B. $12:58$ PM
• C. $1:00$ PM
• D. $2:00$ PM

Answer 1

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: $B$

Comments

wrong approach, those 4hrs are faulty clock hours the real time is not passed 4hrs

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For 4 hrs :  4hrs 2.5 mins (Faulty)

Then  x : 4 hrs (Faulty)

So 4 hrs - X comes to about 2.47 mins

So the total extra time is 1 hr 2.47 mins. So Real time is 2 pm - 1hr 2.47 mins ~= 12:58 PM

Answer 2

$11^{th} july=9 AM$

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

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

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

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

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

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$24H\Rightarrow 15min(gain)$

$4H\Rightarrow ?min$

$?=2.5min(gain)$

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

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

Comments

Best answer :)

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someone plz help . i am not able to understand.

Answer 3

Real 24 h → Clock shows 24 h 15 min = 1455 min
Real 1440 min → Clock 1455 min

Clock runs faster by factor:

Clock / Real = 1455 / 1440 = 97 / 96

So: Real time = Clock time × (96 / 97)

From 11 July 9 AM → 15 July 2 PM

Days difference:

11 → 12 → 13 → 14 → 15 = 4 days
9 AM → 2 PM = 5 hours

Total clock elapsed = 4 days 5 hours = 101 hours

Convert to real:

Real elapsed = 101 × 96 / 97 ≈ 99.96 hours ≈ 99 h 58 min

So correct time:

Start = 11 July 9 AM
Add 99 h 58 min = 4 days 3 h 58 min

= 15 July 12 : 58 PM

Answer: 12 : 58 PM (Option B)