Question

Three candles which can burn, 60 minutes, 80 minutes and 100 minutes respectively are lit at different times. All the candles are burning simultaneously for 30 minutes, and there is a total of 40 minutes in which exactly one is burning. For how many minutes are exactly two candles burning?

Answer 1

55 minutes.
.
The total burn time of the candles = 60 + 80 + 100 = 240 minutes.
During that burn time either one, two or three candles are burning.
.
During 30 minutes all three candles burn = 90 minutes burn time.
During 40 minutes only one candle burns = 40 minutes burn time.
.
That leaves (240 - 90 - 40 = ) 110 minutes of burn time during which two candles are burning
=> 110 / 2 = 55 minutes long.

Comments

So u r saying there are 2 candles with burn time 55+30(85) min. But there is only one candle has length sufficient for 85 min. So u should reconsider ur solution

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My solution is correct. You make the incorrect assumption that the 55 min 2 candle burn time has to come from the same candles. This is not so.
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Let's say candle A = 60 minutes.
Candle B = 80 minutes.
Candle C = 100 minutes.
.
We lit candle B and let it burn for 25 minutes (25 min 1 candle).
We then lit candle C and let them together burn for 25 minutes (25 min 2 candles).
We then lit candle A. After 30 minutes candle B is gone (30 min 3 candles)
After another 30 minutes candle A is gone (30 min 2 candles).
After another 15 candle C is also gone (15 min 1 candle).
This gives a total of 40 min 1 candle + 55 min 2 candles + 30 min 3 candles.