Answer:
The original fraction is \frac{18}{30}
Step-by-step explanation:
Let the original fraction be \frac{x}{y}.
It is given that 2 is added to the numerator and 5 is subtracted from the denominator. Then the fraction will become \frac{x+2}{y-5}.
After the addition & subtraction the original fraction become \frac{4}{5}
According to problem,
\frac{x+2}{y-5} = \frac{4}{5}
or, 5 X (x+2) = 4 X (y-5 )
or, 5x + 5X2 = 4y - 4X5
or, 5x + 10 = 4y - 20
or, 5x -4y + 10+20 = 0
or, 5x - 4y + 30 = 0 ............equation 1
Further is is given that the original fraction is \frac{3}{5}
So, \frac{x}{y} = \frac{3}{5}
or, 5x = 3y ..........................equation 2
Putting the value of 5x in equation number 1, we get
3y - 4y +30 = 0
or, -y = -30
or, y = 30
Putting y= 30 in equation number 2 , we get
5x = 3y
or, 5x = 3 X 30
or x = 18
Therefore the original fraction is \frac{18}{30}
Thank you..!!
