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

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Senior SC Moderator
Joined: 14 Nov 2016
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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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22 Feb 2017, 18:14
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95% (hard)

Question Stats:

56% (02:21) correct 44% (02:11) wrong based on 180 sessions

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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. $$\frac{4t}{5}$$

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Joined: 07 Dec 2014
Posts: 1020
There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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22 Feb 2017, 20:59
2
2
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
Manager
Joined: 17 May 2015
Posts: 232
Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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04 Jun 2017, 04:58
2
1
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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11 Aug 2017, 03:54
2
2
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

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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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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

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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Joined: 02 Nov 2015
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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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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

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

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Intern
Joined: 15 Mar 2017
Posts: 42
Location: India
GMAT 1: 720 Q50 V37
GPA: 4
Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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11 Aug 2017, 10:46
1
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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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

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

Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app

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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Senior Manager
Joined: 02 Apr 2014
Posts: 485
GMAT 1: 700 Q50 V34
Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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19 Feb 2018, 14:01
Let height of candles be, 3L
if candle B, burnt L length(Remaining length - 2L), candle A would have burnt 2L length (remaining length - L).
So when candle B has burnt L length, its height will be twice as that of candle A.
Time taken for full length (3L) candle B to burn = 2t
Time taken for L length of candle B to burn = 2t/3
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Joined: 09 Nov 2015
Posts: 30
Re: There are 2 candles with the same height. It takes t mins for A to bur [#permalink]

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21 Feb 2018, 00:35
Let the required time be X mins. In 1 min Candles A and B will burn (1/t)th and (1/2t)th of their respective lengths. In X mins, they will burn (X/t)th and (X2t)th of their lengths. So, remaining lengths of A and B will be (1-(X/t)) and (1-(X/2t)) respectively. But after X mins. height of B will be twice that of A. So,
2(1-(X/t))=1-(X/2t). Solving we get X=2t/3. Ans: B
Re: There are 2 candles with the same height. It takes t mins for A to bur   [#permalink] 21 Feb 2018, 00:35
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