Question

Anil takes 6 days less than the time taken by Varun to finish a piece of work. If both Anil and Varun together can finish the same work in 4 days, find the time taken by Varun to finish the work independently.

Answer 1

LET ANIL BE x
AND VARUN BE y
  
According To Question
    x=y-6
    y=x+6..........(1)

ANIL TAKES 1/x
VARUN TAKES 1/y

NOW, 
   1/x+1/y=1/4
    x+y/xy=1/4............(2)
put the value of x in eq. 2
   x+x+6/x(x+6)=1/4
   2x+6/x²+6x=1/4
NOW CROSS MULTIPLY
    8x+24=x²+6x
    x²+6x-8x-24
    x²-2x-24
    x²-6x+4x-24
    x(x-6)+4(x-6)
     (x+4)(x-6)
    x=-4(neg)    x=6
ANIL TAKE 6DAYS FINISH WORK SEPARATELY 

NOW 
VARUN TAKE (X+6) FINISH WORK SEPARATELY
 ∴ 6+6=12


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Answer 2

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