Melting Candles | Puzzles for Interview - Interview Preparation PDF Download

Introduction

This puzzle involves two candles of equal length but different thicknesses. The thicker candle lasts for 6 hours while the thinner one lasts for 2 hours less. If you light both candles at the same time and return to find the thicker one is twice the length of the thinner one, how long ago did you light the candles?

Solution

To solve this problem, you need to find the number of hours it takes for the thicker candle to become twice the length of the thinner candle.
After each hour, (1/6) of the thicker candle melts while (1/4) of the thinner one melts. 
After 1 hour, (5/6) of the thicker candle remains while (3/4) of the thinner candle remains. 
After 2 hours, (4/6) of the thicker candle remains while (2/4) of the thinner candle remains. 
After 3 hours, (3/6) of the thicker candle remains while (1/4) of the thinner candle remains. 
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. 
Therefore, the person lit the candles 3 hours ago.

Conclusion

The Melting Candles Puzzle can be solved in two ways. The first solution involves analyzing the problem hour by hour, while the second solution involves using algebraic equations. Both solutions lead to the same answer, which is that the person lit the candles 3 hours ago.