On a diwali eve two candels were there one was longer than other by 3 cm . the longer one was lighted at 5.30 p.m and the shorter one at 7 p.m at 9.30 p.m both were of same length . the longer one burn out at 11 p.m and the shorter one at 11.30 p.m.
It is on simultaneous linear equation
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)
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
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