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655-705 (Hard)|   Geometry|      
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Bunuel
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Two cylindrical candles of the same height and diameter burn at the sa 06 Dec 2017, 23:17
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66% (02:34) correct 34% (02:34) wrong based on 105 sessions

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Two cylindrical candles of the same height and diameter burn at the same uniform rate. Each takes 4 hours to be consumed. If the first candle is lit at 8.00 p.m and the second at 9.00 p.m, at what time will the second candle be exactly 3 times as tall as the first?

(A) 9.30 p.m
(B) 10.00 p.m
(C) 10.30 p.m
(D) 11.00 p.m
(E) 11.30 p.m
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Two cylindrical candles of the same height and diameter burn at the sa 07 Dec 2017, 00:08
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Going by options, at 11.30 , candle 1 will be 1/8th of length, candle 2 will be 3/8 of length. Option E

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Two cylindrical candles of the same height and diameter burn at the sa 07 Dec 2017, 01:39
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Bunuel
Two cylindrical candles of the same height and diameter burn at the same uniform rate. Each takes 4 hours to be consumed. If the first candle is lit at 8.00 p.m and the second at 9.00 p.m, at what time will the second candle be exactly 3 times as tall as the first?

(A) 9.30 p.m
(B) 10.00 p.m
(C) 10.30 p.m
(D) 11.00 p.m
(E) 11.30 p.m
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Assume both the candles be of height 40 cm and their burn rate be 10 cm/ hr

9:00 PM (Candle Left) A 30 Cm B 40 Cm
10:00 PM (Candle Left) A 20 Cm B 30 Cm
11:00 PM (Candle Left) A 10 Cm B 20 Cm
11:30 PM (Candle Left) A 5 Cm B 15 Cm
E
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Two cylindrical candles of the same height and diameter burn at the sa 07 Dec 2017, 06:13
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Bunuel
Two cylindrical candles of the same height and diameter burn at the same uniform rate. Each takes 4 hours to be consumed. If the first candle is lit at 8.00 p.m and the second at 9.00 p.m, at what time will the second candle be exactly 3 times as tall as the first?

(A) 9.30 p.m
(B) 10.00 p.m
(C) 10.30 p.m
(D) 11.00 p.m
(E) 11.30 p.m
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Let the two candles are of 40 cm each
At 9 pm C1 = 3/4(40) = 30 cm and C2 = 40 cm

Let x and y be the length of candle that needs to be consumed from C1 and C2 respectively for the second candle to be exactly 3 times as tall as the first.
40-x = 3(30-y)
Since both the candles length are considered at 9 pm and are getting consumed at same rate, x= y
y= 25

fraction of candle 2 left : 25/40 = 5/8
1 candle gets consumed in 4 hrs,
time taken for 5/8 candle to consume = 4*(5/8) = 2.5 hrs

time = 9pm +2.5 hrs = 11.30 pm
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Two cylindrical candles of the same height and diameter burn at the sa 26 Jun 2021, 19:45
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Let the volume of each Candle (X and Y) be equal to = 1 cubic unit

Rate of Candle X = Rate of Candle Y = (1 candle) / (4 hours) = 1/4

Let T = number of hours it takes for Candle X to be (1/3) the Height of Candle Y

(Rate of Burning) * (Time) = Amount of Candle Burnt

And

The Height of each Candle after some amount of time burning = 1 - (Amount of Candle Burnt


Candle X: starts burning at 8 PM, with a 1 hour head-start

Amount of Candle X Burnt = (1/4) * (T + 1)

Height of Candle X = 1 - [ (1/4) (T + 1)]


Candle Y starts burning at 9 PM

Amount of Candle Y burnt = (1/4) * (T)

Height of Candle Y = 1 - (1/4)*T

Need:
Height of Candle X = (1/3) (Height of Candle Y)

Plugging in the expressions we found above:


[1 - (1/4) (T + 1)] = (1/3) * [1 - (1/4)T]


1 - (T/4) - (1/4) = (1/3) - (T/12)

(3/4) - (1/3) = (T/4) - (T/12)

5/12 = 2T/12

5 = 2T

T = 2.5 hours


9:00 PM + 2.5 hours = 11:30 PM

E

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Two cylindrical candles of the same height and diameter burn at the sa 05 Apr 2025, 05:23
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