Question

Find the fraction which becomes to 2/3 when the numerator is increased by 2 and equal to 4/7 when the denominator is increased by 4.

Answer 1

let the fraction be x/y.

According to question,

x/y+2 =2/3 -----------(1)

Again,

x/y+4 =4/7-------------(2)

Solving eq. (1)

x/y+2=2/3-------(1)

3x=2y+4 {By cross multiply}

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

Solving eq.(2)

x/y+4=4/7---------(2)

7x=4y+16 {By cross multiply}

7x-4y=16--------------(4)

Now, Solving eq.(3)&(4)

3x-2y=4----------×7

7x-4y=16--------×3

so, the eq.(3)&(4) will now be

21x-14y=28-------(5)

21x-12y=48-------(6)

- +