Question

The denominator of a fraction exceeds its numerator by 4. If the numerator & denominator are both increased by 3, the new fraction becomes 4/5. Find the original fractions.

Answer 1

y=x+4.......(i)

x+3/y+3=4/5
5x+15=4y+12

Putting (i)
5x+15=4(x+4)+12
5x+15=4x+16+12
x=13

putting x in (i)
y=13+4
y=17
Fraction= x/y= 13/17

Answer 2

Answer:

The original fraction is 13 / 17

Step-by-step-explanation:

Let the numerator be x.

And the denominator be y.

Original fraction = x / y

From the first condition,

y = x + 4 - - ( 1 )

From the second condition,

( x + 3 ) / ( y + 3 ) = 4 / 5

=> 5 ( x + 3 ) = 4 ( y + 3 )

=> 5x + 15 = 4y + 12

=> 5x - 4y = 12 - 15

=> 5x - 4y = - 3

=> 5x - 4 ( x + 4 ) = - 3 - - ( From 1 )

=> 5x - 4x - 16 = - 3

=> x = - 3 + 16

=> x = 13

Put x = 13 in ( 1 )

y = x + 4

=> y = 13 + 4

=> y = 17

Numertaor ( x ) = 13

Denominator ( y ) = 17

Therefore,

The original fraction = 13 / 17