Two candles of equal height but …
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Sia ? 5 years, 11 months ago
Let height of each candle = x unit.
First candle burns off in 6 hours.
Second candle burns off in 8 hours.
Height of 1st candle after burning for 1 hr = x6unit
and height of 2nd candle after burning for 1 hr = x8unit
Let the required time =y hrs.
Length of 1st candle burnt after y hrs = y×x6unit
Height of 1st candle left = (x−xy6)
Length of 2nd candle burnt after y hrs = (y×x8)unit
Height of 2nd candle left = (x−xy8)
According to the question,
Height of 1st candle = 12×Height of 2nd candle
⇒x−xy6=12(x−xy8)
⇒x(1−y6)=12x(1−y8)
1−y6=12(1−y8)
⇒2−y3=1−y8
2−1= y3−y8
1 = 8y−3y24
⇒ 24=5y
⇒ y= 245
y=4.8hours=4 hours 48 minutes.
3Thank You