There are two candles of equal lengths and of different thickness..?

Question

There are two candles of equal lengths and of different thickness. The thicker one lasts of six hours. The thinner 2 hours less than the thicker one. Ramesh lights the two candles at the same time. When he went to bed he saw the thicker one is twice the length of the thinner one. How long ago did Ramesh light the two candles

Answer 1

Let length of thinner candle = l1 ;radius of thinner candle = r1
Let length of thicker candle = l2 ;radius of thicker candle = r2

At first : l1 = l2

Volume ratio = pi*r2²*l2/pi*r1²*l1

Time of burning is proportional to volume ratio

Let the time be x hrs for which both burn

Thicker burns 6 hours

Thinner burns 4 hours

r2²/r1² = 6/4 = 3/2

After x hours l2 = 2*l1
l2/l1 = 2

Volume ratio after x hrs = l2*r2² /l1*r1² = 3*2/2 = 3

Time of burning is proportional to volume ratio

Time x = 3 hours

Ramesh light the two candles after 3 hours

Answer 2

at time t,
The thick candle length is = initial length x ( 1-t/6 )
The thin candle length is = initial length x ( 1-t/4 )

and the thick candle lenth is twice of thin candle, thus
initial length x ( 1-t/6 ) = 2 x initial length ( 1-t/4 )
t=3 (hours)

Hence, after 3 hours Ramesh light the two candles, the thick candle remains twice the length of the thinner one.

Answer Checking:
After 3 hours,

The thick candle length = 1/2 of initial length [as (1-3/6)=1/2]
The thin candle length = 1/4 of initial length [as (1-3/4)=1/4]
Hence, after 3 hours, the thick candle is twice of the thin candle's length [as 1/2 = 2 x 1/4].

Answer 3

2 hours

Answer 4

90 min. ago

Answer 5

tat's a good question........ answer may be 74 mins

Answer 6

2hrs