Question

sum of a numerator and denominator of a fraction is 8 add 3 to both numerator and denominator and the fraction will be 3/4 find the fraction​

Answer 1

Answer:

The fraction is 3/5

let the numerator be x and denominator be y

According to the given question,

sum of num and den is 8 i.e.

x + y = 8 —(1)

Add 3 to both num and den

x+3 = 3

y+3 4

By cross multiplication,

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

4x + 12 = 3y + 9

4x - 3y = 9 - 12

4x - 3y = -3 —(2)

solving (1) & (2),

x + y = 8 ]×4

4x + 4y = 32

4x - 3y = -3

- + +

By elimination,

7y = 35

y = 5

put y = 5 in (1),

x + y = 8

x = 8-5

x = 3

Hence, the fraction is 3/5

Answer 2

let the numeratoros is x and denominator is y

ATQ

x+y = 8

therefore, x+3= 3

y+3 4

or 4(x+3) =3(y+3)

or 4x+12=3y+9

or 4x-3y=-3......(2)

solving equation (1)and(2),we have x=3and y=5

thus, the required fraction is 3/5