Question

if one add both numutor and denominor of the given fraction it become 4/5.if we 5 is subtraction from both the numutor and denominor fraction become 1/2. find the fraction.​

Answer 1

Step-by-step explanation:

let the fraction be

$\frac{x}{y}$

as per the given condition, the equation will be,

$\frac{x + 1}{y + 1} = \frac{4}{5}$

by cross multiplying,

5(x+1) = 4(y+1)

5x+5 = 4y+4

5x = 4y+4-5

5x = 4y - 1

$x = \frac{4y - 1}{5}$

consider it as equation(1).

as per the second given condition, the equation is,

$\frac{x - 5}{y - 5} = \frac{1}{2}$

by cross multiplying,

2(x-5) = 1(y-5)

2x - 10 = y - 5

2x = y - 5 + 10

2x = y + 5. consider it as equation (2).

putting equation (1) in equation (2), we get,

$2( \frac{4y - 1}{5} ) = y + 5$

$\frac{8y - 2}{5} = y + 5$

$8y - 2 = 5(y + 5)$

8y - 2 = 5y + 25

8y - 5y = 25 + 2

3y = 27

y = 27/3

y = 9. equation (3)

substituting the value of y from equation (3) to equation (2)

2x = y + 5

2x = 9 + 5

2x = 14

x = 14 / 2

x = 7

Therefore, we considered the fraction to be,

$\frac{x}{y}$

So, the fraction will be

$\frac{7}{9}$