Clock puzzle.. Bit tricky

Twin Sisters A and B bought 2 wristwatches at 12 p.m .

An Hour later , A's watch reads 1:02 p.m while B's watch reads 12:56 p.m.

Later , on same day : If A's watch reads 10 p.m then at that time what is the reading on B's Watch ..?

Options:

a)exactly 9.00pm

b)approximately 9.00pm

c)exactly 9.20pm

d)approximately 9.20pm

e)exactly 9.40pm

f)approximately 9.40pm

g)None of these

Answer : NOT exactly known .

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B’s watch covers $56$ minutes while A’s covers $62$, so B’s watch runs $\frac{56}{62}=\frac{28}{31}$ times as fast as A’s. At the time in question A’s watch has covered $10$ hours, or $600$ minutes, so B’s has covered

$$\frac{28}{31}\cdot600=\frac{16800}{31}\approx541.9355$$

minutes, or a little under $9$ hours and $2$ minutes. The correct answer is therefore (b).

Added: Note that at $10$ p.m. A’s watch reads $10:20$, and B’s reads $9:20$. It was roughly $20$ minutes earlier when A’s watch read $10:00$ p.m., and at that point B’s also read roughly $20$ minutes earlier, or around $9:00$ p.m. This rough calculation already shows that the answer should be (a) or (b). And since A’s watch runs faster than B’s, backing up A’s watch by $20$ minutes to $10:00$ p.m. must back up B’s by less than $20$ minutes to something a little after $9:00$ p.m. This gets us the answer (b) without any messy arithmetic.

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Thanks.,.....:) – Jay Teli Feb 3 '13 at 23:57
You’re welcome. – Brian M. Scott Feb 4 '13 at 0:00

My Approach : I tried using methods that lead me to different answers :

One of which i fell MAY be correct is using the logic that there will be difference of multiples of 6 min( n hours => 6n min gap ) in the readings .

After 10 hours , gap would be 60 mins : A=10pm and B=9pm thus a is answer as per me ; some of my friends have got c , d .

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the twin sisters bought the watches but when did they set the time? so B's watch continues to show 6 minutes minus difference Time A =10:00 pm B = 9:54 PM

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answer is g. non of these – HS Bhatti Feb 19 at 12:07