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There are 2 candles with the same height. It takes t mins for A to bur

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There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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New post 22 Feb 2017, 18:14
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There are 2 candles with the same height. It takes t mins for A to burn, and it takes 2t mins for B to burn. When the candles are burnt at the same time, how many minutes did it take for the height of B to be twice the height of A?

A. \(\frac{t}{3}\)      

B. \(\frac{2t}{3}\)

C. \(\frac{t}{2}\)

D. \(\frac{3t}{4}\) 

E. \(\frac{4t}{5}\)
[Reveal] Spoiler: OA

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There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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New post 22 Feb 2017, 20:59
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AustinKL wrote:
There are 2 candles with the same height. It takes t mins for A to burn, and it takes 2t mins for B to burn. When the candles are burnt at the same time, how many minutes did it take for the height of B to be twice the height of A?

A. \(\frac{t}{3}\)      

B. \(\frac{2t}{3}\)

C. \(\frac{t}{2}\)

D. \(\frac{3t}{4}\) 

E. \(\frac{4t}{5}\)


if A burns twice as fast as B,
then 2/3 of A and 1/3 of B will burn in the same time
and the remaining 2/3 of B will be twice the height of the remaining 1/3 of A
fraction of work done by A=2/3
rate of A=1/t
(2/3)/(1/t)=2t/3 minutes
B

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Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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hazelnut wrote:
There are 2 candles with the same height. It takes t mins for A to burn, and it takes 2t mins for B to burn. When the candles are burnt at the same time, how many minutes did it take for the height of B to be twice the height of A?

A. \(\frac{t}{3}\)      

B. \(\frac{2t}{3}\)

C. \(\frac{t}{2}\)

D. \(\frac{3t}{4}\) 

E. \(\frac{4t}{5}\)


Hi,

Let the height of two candles is 1. Let the required time is x minutes.

Height of candle A after x minutes = \(1 - \frac{x}{t}\)
And
Height of candle B after x minutes = \(1 - \frac{x}{2t}\)

From the given condition:

\(2*(1 - \frac{x}{t}) = 1 - \frac{x}{2t}\)

=> \(\frac{2x}{t} - \frac{x}{2t} = 1\)

=> \(\frac{4x - x}{2t} = 1\)

=> \(x = \frac{2t}{3}\)

Thanks.

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Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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hazelnut wrote:
There are 2 candles with the same height. It takes t mins for A to burn, and it takes 2t mins for B to burn. When the candles are burnt at the same time, how many minutes did it take for the height of B to be twice the height of A?

A. \(\frac{t}{3}\)      

B. \(\frac{2t}{3}\)

C. \(\frac{t}{2}\)

D. \(\frac{3t}{4}\) 

E. \(\frac{4t}{5}\)



Let h be the height of the candle.
So, A burns at a speed of h/t
B burns at a speed of h/2t

Let the required time be T
so A's height after T min = h - (h/t)*T
B's height after T min = h-(h/2t)*T


h-(h/2t)*T = 2* (h - (h/t)*T)
h = 3/2*(h/t)*T
T = 2/3* t

Answer B

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There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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New post 11 Aug 2017, 06:37
Assume t=30 seconds.
Let the height of the candle be 300 unit.
Candle A which burns in 30 seconds, burns at a rate of 10 units/second.
Similarly Candle B which burns in 2t(60) seconds, burns at a rate of 5 units/second

Now evaluating the answer choices,

Option A(\(\frac{t}{3}\)) gives time of burning at 10 seconds
In 10 seconds, Candle A burns 100 units making the height of the candle 200 units.
Candle B burns 50 units, making the height 250 units.
Candle B's height is not equal to twice Candle A's height.

Option B(\(\frac{2t}{3}\)) gives time of burning at 20 seconds
In 10 seconds, Candle A burns 200 units making the height of the candle 100 units.
Candle B burns 100 units, making the height 200 units.

Candle B's height is equal to twice Candle A's height. That is our answer!(Option B)
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Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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New post 11 Aug 2017, 09:52
shashankism wrote:
hazelnut wrote:
There are 2 candles with the same height. It takes t mins for A to burn, and it takes 2t mins for B to burn. When the candles are burnt at the same time, how many minutes did it take for the height of B to be twice the height of A?

A. \(\frac{t}{3}\)      

B. \(\frac{2t}{3}\)

C. \(\frac{t}{2}\)

D. \(\frac{3t}{4}\) 

E. \(\frac{4t}{5}\)



Let h be the height of the candle.
So, A burns at a speed of h/t
B burns at a speed of h/2t

Let the required time be T
so A's height after T min = h - (h/t)*T
B's height after T min = h-(h/2t)*T


h-(h/2t)*T = 2* (h - (h/t)*T)
h = 3/2*(h/t)*T
T = 2/3* t

Answer B

Very lucid explanation.
Thanks . Very helpful for me..

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Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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New post 11 Aug 2017, 10:46
We can calculate the answer by simply plugging the values
Let's assume the height of each candle is 60cm and time taken to burn candle A is 60sec and time to burn B is 120sec

In 30 secs: A will be of height 30 cm and B will be of the height 45cm. It's still not double. Time taken would be a bit more for the length to double.
IN 40 secs: A will be of height 20 cm and B will be of the height 40cm. Time elapsed to double the height was 40 secs.

Our assumed time "t" was 60 secs. Checking the values, we get: time required=2/3 ( total time)
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Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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New post 11 Aug 2017, 11:28
kumarparitosh123 wrote:
shashankism wrote:
hazelnut wrote:
There are 2 candles with the same height. It takes t mins for A to burn, and it takes 2t mins for B to burn. When the candles are burnt at the same time, how many minutes did it take for the height of B to be twice the height of A?

A. \(\frac{t}{3}\)      

B. \(\frac{2t}{3}\)

C. \(\frac{t}{2}\)

D. \(\frac{3t}{4}\) 

E. \(\frac{4t}{5}\)



Let h be the height of the candle.
So, A burns at a speed of h/t
B burns at a speed of h/2t

Let the required time be T
so A's height after T min = h - (h/t)*T
B's height after T min = h-(h/2t)*T


h-(h/2t)*T = 2* (h - (h/t)*T)
h = 3/2*(h/t)*T
T = 2/3* t

Answer B

Very lucid explanation.
Thanks . Very helpful for me..

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Thanks kumarparitosh123, I will be coming up with solutions of more problems once I take GMAT. I will target some really good questions. :)
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Re: There are 2 candles with the same height. It takes t mins for A to bur   [#permalink] 11 Aug 2017, 11:28
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