Question

1. If 2 is added to both the numerator and
denominator of a rational number its value
becomes double. If 8 is added to both the
numerator and denominator its value becomes
triple. Find the number.​

Answer 1

Answer:

1/4

Step-by-step explanation:

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