find a fraction which is doubled when 2 is added to both numerators and Denominators and tripled when 8 is added to denominator and numerator.Find the Fraction

Asked by Shubham Verlekar | 9th Jul, 2013, 08:41: PM

Expert Answer:

Let numerator be equal to x and denominator be equal to y. 
 
Then, x/y would represent the fraction. 

So, (x+2)/(y+2)  = 2x/y 
xy + 2y = 2xy + 4x
2y = xy + 4x  (1)
 
Also, (x+8)/(y+8)  = 3x/y 
xy + 8y = 3xy  + 24x
8y = 2xy + 24x
4y = xy + 12x  (2)
 
Subtracting 1 and 2. 
 
2y = 8x
y = 4x
 
Substituting this back in 1
2(4x) = x(4x) + 4x
8x = 4x^2 + 4x
4x = 4x^2 
x = 1 or x = 0 
Since, x can't be equal to 0, so x =1 
y = 4(1) = 4
 
So, fraction= 1/4.

Answered by  | 9th Jul, 2013, 11:00: PM

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