Melting Candles | Puzzle Last Updated : 18 Jan, 2023 Improve Improve Like Article Like Save Share Report Problem Statement: There are two candles of equal lengths but of different thicknesses. The thicker candle lasts for 6 hours while the thinner one lasts for 2 hours lesser 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? Solution: According to the problem statement, the thicker candle lasts for 6 hours while the thinner one lasts for 2 hours lesser 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 lesser 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(Candle 1) one. Suppose remaining length of Candle 1 = x. So, 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. Like Article Suggest improvement Previous Puzzle | Six Houses P, Q, R, S, T, and U Next Puzzle 47 | Red Hat vs Blue Hat Share your thoughts in the comments Add Your Comment Please Login to comment...