Question

if one is added to both the numerator and denominator of a given fraction it becomes 4 by 5 if however 5 is subtracted from both the numerator and denominator fraction becomes 1 by 2 find the fraction

Answer 1

let the fraction be x/y

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

=> 5x-4y+1=0

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

=> 2x-y-5=0

by solving these eqns...

x=7

y=9

x/y=7/9

Answer 2

SOLUTION :

Let the numerator be x and denominator be y

Fraction = numerator/denominator  

Fraction =  x/y

A.T.Q

1st case :

x +1 / y +1 = 4/5

5(x +1)  = 4(y +1)  

5x + 5 = 4y + 4

5x - 4y = 4 -5

5x - 4y =  -1.............(1)

2nd case :

x - 5 / y - 5 = 1/2

2 (x - 5 )  = 1 (y - 5)  

2x - 10 = y - 5

2x - y = - 5 +10

2x - y = 5…………(2)

Multiply eq 2 by 4

8x - 4y = 20………..(3)

On Subtracting eq 1 from eq 3

8x - 4y = 20

5x - 4y =  -1

(-)  (+)    (+)

------------------

3x = 21

x = 21/3

x = 7

Put this value of x in eq 1

5x - 4y =  -1

5(7) - 4y = -1

35 - 4y = -1

35 +1 = 4y

36 = 4y

y = 36/4

y = 9

Fraction = x/y = 7/9

Fraction = 7/9

Hence, the fraction is 7/9

HOPE THIS ANSWER WILL HELP YOU...