Puzzle | Melting Candles

There are two candles of equal length but of different thicknesses. The thicker candle lasts for 6 hours, while the thinner one lasts for 2 hours less than the thicker one. A person lights the two candles at the same time and goes to play. After returning home, the person saw that the thicker candle was twice the length of the thinner one.

How long ago did the person light the two candles?

Check if you were right - full answer with solution below.

Solution: 

According to the problem statement, the thicker candle lasts for 6 hours, while the thinner one lasts for 2 hours less than the thicker one.

Therefore, the thinner candle lasts for 4 hours.

The problem reduces to finding the number of hours it takes for the thicker candle to become twice the length of the thinner candle.

Analyzing the problem hour by hour, after each hour (1/6) part of the thicker candle is melted, while (1/4) part of the thinner candle is melted.

• After 1 hour, (5/6) part of the thicker candle remains, while (3/4) part of the thinner candle remains.
• After 2 hours, (4/6) part of the thicker candle remains, while (2/4) part of the thinner candle remains.
• After 3 hours, (3/6) part of the thicker candle remains, while (1/4) part of the thinner candle remains.

On observing carefully, it can be found that at the end of 3 hours the remaining part of the thicker candle is (1/2) while it is (1/4) for the thinner candle i.e., the thicker candle is twice the length of the thinner one.

Another Approach : 

Assume Candle 1 is thinner and Candle 2 is thicker. Suppose Length of Candle 1 = L and Length of Candle 2 = L

According to the problem statement, the thicker candle lasts for 6 hours, while the thinner one lasts for 2 hours less than the thicker one. Therefore, the thinner candle lasts for 4 hours.

After returning home, the person saw that the thicker candle(Candle 2) was twice the length of the thinner one(Candle 1).

Suppose the remaining length of Candle 1 = x. So, the remaining length of Candle 2 = 2x.

For Candle 1, Time taken for melting (L - x) part = T1 = ((L - x)*4)/L

Similarly, For  Candle 2, Time taken for melting (L - 2x) part = T2 = ((L - 2x)*6)/L

We know that T1 andT2 are same. So, T1 = T2

So, By solving above two equation, we  get the relation L = 4x

So, Total Length of Candle 1 and Candle 2 are 4x.

So, For Candle 2, (4x - 2x) = 2x part is melting that means half of the Candle 2 is melting. So Time taken for melting half of the Candle 2 = 6 / 2 = 3 hour.

So, person light the two Candles 3 hours ago.