Puzzle | Melting Candles

There are two candles placed on a table. Both candles have the same initial length, but they are of different thicknesses.

Assuming each candle burns uniformly:

• The thicker candle burns completely in 6 hours.
• The thinner candle burns completely in 4 hours.

Both candles are lit at the same time. After some time, you come back and observe that the thicker candle is exactly twice as long as the thinner candle.

How much time has passed since the candles were lit?

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

Solution: 

Both candles have the same initial length.

• Thicker candle burns completely in 6 hours → burns 1/6 of its length per hour.
• Thinner candle burns completely in 4 hours → burns 1/4 of its length per hour.

Let time passed = t hours

Remaining length after t hours:

• Thicker candle = 1 − t/6
• Thinner candle = 1 − t/4

According to the question:

Thicker candle = 2 × Thinner candle

So, 1 − t/6 = 2(1 − t/4)

Now solve: 1 − t/6 = 2 − t/2

Bring terms together:

1 − t/6 − 2 + t/2 = 0

-1 + (t/2 − t/6) = 0

Take LCM: t/2 − t/6 = (3t − t)/6 = 2t/6 = t/3

So, -1 + t/3 = 0

t/3 = 1

t = 3

3 hours have passed since the candles were lit.

Shortcut (Logical Way):

After 3 hours:

• Thicker candle burns 3/6 = 1/2 → remaining = 1/2
• Thinner candle burns 3/4 → remaining = 1/4

So, thicker = 1/2 and thinner = 1/4
Clearly, thicker candle is twice the thinner one

Hence, time = 3 hours.