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 It is on simultaneous linear equation
 Entrance Exam
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Let the length of the shorter candle be x.cm
Then, the length of the longer candle = (x + 3) cm
The shorter candle burn out in 9/2 hours.
So, the rate of burning of shorter candle = 2x /9
Similarly the longer candle burns out in 11/2 hours.
So, the rate of burning of longer candle = 2(x+3) / 11
Let us compute the length of the shorter candle after 5/2 hours which is
Length of candle burnt after 5/2 hours = 2x/9 x (5/2)
= 5x/9
Actual length of shorter candle after 5/2 hours = x  5x/9 = 4x/9 .....................(1)
Now, let us compute the length of the longer candle after 4 hours which is
Length of candle burnt after 5/2 hours = 2(x+3)/11 x 4
= 8(x+3)/11
Actual length of longer candle after 4 hours = (x+3)  (8(x+3)/11)
= (3(x+3))/11 .................................(2)
Now according to the question, the length of the two candles at 9:30 are equal.
Therefore, 4x/ 9 = 3x + 9/ 11
⇒ 44x = 27x + 81
⇒ 14 x = 81
So, x = 5.78 cm