late one night a man was studying for nda exam when lights went out he lit two candles of equal length one thicker than the other the thicker candle is supposed to last for 6 hrs and thin 2 hrs less when he went to sleep the thick candle was twice long as the thin one for how long all study by candle
Answers
Answer:
Let the length of both the candles be x cmNow speed of burning of thick candle will be x6cm/hourAnd speed of burning of thin candle x4 cm/hourNow let the new length after burning of thinner candle be y cmHence according to question ,new length of thicker candle be 2y cmDistance travelled by the thinner candle will be (x−y) cmDistance travelled by the thicker candle will be (x−2y) cmLet the time taken to burn be t hoursNow as we know distance = speed×time∴(x−y)=x4×t..........(1)(x−2y)=x6×t............(2)Subtracting (2) from (1) we gety=t(x4−x6)⇒y=t(x12)Puttinh y=t(x12) in (1) we getx=x4t+x12t⇒x=4x12t⇒t=3 Hence Pinku studied for 3 hours in the candle light
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Question :
Late one night a man was studying for his exam when lights went out . He lit two candles of equal length , one thicker than the other . The thicker candle is supposed to last for 6 hrs and the thin one for 2 hrs less. When he went to sleep , the thick candle was twice long as the thin one. For how long did he study by candle ?
Answer :
The man studied for 3 hours by candle.
Given :
Thick candle lasts for 6hrs
Thin candle lasts for 2hours less
To find :
how long did the man study by candle
Solution :
Let the initial length of both the candles be = x
The thick candle light for
6×60mins
=3600mins
The thin candle light for
= (6-2) × 60mins
=240mins
Let n be the time he studied by candle
Length of thick candle after n minute = x- n(x/3600)
Length of thin candle after n minute = x- n(x/2400)
Thus , when he went to sleep :
Length of thick candle = 2(length of thin candle)
x- n(x/3600) = 2(x- n(x/2400))
=>1- n/3600 =2- 2n/2400
=>n=180 mins
= 3 hours
Hence, the man studied for 3 hours by candle.
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