The ratio of the numerator to the denominator of a certain fraction is three to five. if two is added to the numerator and five is subtracted from the denominator, the new fraction reduces to four-fifths. find the original fraction.

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..!!