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Melting Candles | Puzzle
• Difficulty Level : Basic
• Last Updated : 04 Apr, 2021

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.
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