August 2011

# Solution

The candles had burnt for 3 hours and 45 minutes.

The candles, initially, are of the same length, say, "l" units (centimetres or inches or whatever). Let us suppose that the candles had burnt for "t" minutes before lights came on.

The fat candle is supposed to burn for five hours (300 minutes), so in one minute l/300 units of that candle burns off. In "t" minutes, tl/300 units of the candle burns off and the length of the candle remaining is l - tl/300.

The slender candle is supposed to burn for four hours (240 minutes), so in one minute l/240 units of that candle burns off. In "t" minutes, tl/240 units of this candle burns off and the length of the candle remaining is l - tl/240.

Now the fat candle is four times longer than the slender one.

So, l - tl/300 = 4(l - tl/240)

This gives us, (300l - tl)/300 = (240l - tl)/60. So, we get t = 225 minutes which is 3 hours and 45 minutes.

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