Question: Two candles of the same height are lighted at the same time. The first candle is consumed in 4 hours and the second one in 3 hours. Assume that each candle burns at the same rate. In how many hours will the first candle measure twice the height of the second candle?

(A) 1 hour and 12 minutes
(B) 2 hours and 24 minutes
(C) 3 hours and 45 minutes
(D) 4 hours and 10 minutes
(E) 4 hours and 48 minutes

Correct Answer: B
Solution and Explanation:
Approach Solution 1:

After any given time(t), length of first candle= Lt/4
After any given time(t), length of second candle= L−Lt/3

Time(t) after the first candle measure twice the height of the second candle
L−Lt/4= 2*[L−Lt/3]
1−t/4= 2−2t/3
2t/3−t/4= 1
8t−3t/12= 1
5t=12
t=2.4 hours= 2 hours and 24 minutes

Approach Solution 2:

For candle A time taken for 100% bearing= 4 hour
So in 1 hour it burns for 25% (100/4)
So, after 1 hr. 25/100 i.e., 1/4 of it has burn 1
Hence, after x hours, amount burnt= x/4
So, amount left= 1−x/4=4−x/4

Simply for candle B, let no assume that its height is half of candle A after x hours.
So, after x hours, part vemacing= 1-x/3= 3-x/3
According to question,
4-x/4= 1(3-x/3)
i.e, Height of candle A=2×. Height of candle B.
Therefore, 12-3x= 24-8x
=> 5x= 12
x= 12/5
= 2.5
So, after 2.4 hours, the height of candle 4 is twice that of candle B.

Approach Solution 3:
Let, h0=initial height of both candles, t=initial time of burning of both candles, h1=current height of first candle, h2=current height of second candle
=> h1=h0-(h0*t)/4; h2=h0-(h0*t)/3. Putting these eqs in h1=2*h2
=> 1-t/4 = 2(1-t/3)
=> t=12/5 h = 2.4 h = 2h and 24min

“Two candles of the same height are lighted at the same time.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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