Question

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction become 6/5 and if the denominator is double and the numerator is increase by 8, the fraction become 2/5. find the fraction​

Answer 1

Step-by-step explanation:

let numerator=x

denominator=y

fraction =x/y

ATQ _1

2x/y-5=6/5

10x=6y-30

5x-3y=-15 -----------(i)

ATQ _2

x+8/2y=2/5

5x+40=4y

5x-4y=-40-----------(ii)

subtract (i) and (ii)

5x-3y=-15

5x-4y=-40

- + +

___________

0+y=25

___________

y=25

putting this value in eq (i)

5x-3y=-15

5x-3(25)=-15

5x-75=-15

5x=-15+75

5x=60

x=12

hence,

x=12 y=25

Answer 2

Answer:

x=12 ; y = 25

Step-by-step explanation:

let the fraction = x/y

acc. to question

2x/(y-5) = 6/5

2x(5) = 6(y-5)

10x = 6y - 30

10x - 6y = -30 ----------(1)

(x+8)/2y = 2/5

5(x+8) = 2(2y)

5x + 40 = 4y

5x - 4y = -40 ----------(2)

multiply by 2 in eq. 2

2(5x - 4y = -40)

10x - 8y = -80 ---------(3)

on subtaract eq. 1 from 3

10x - 8y = -80

10x - 6y = -30

- + +

0 - 2y = -50

y = -50/(-2)

y = 25

put y in eq. 1

10x - 6y = -30

10x - 6(25) = -30

10x - 150 = -30

10x = -30 + 150

10x = 120

x = 120/10

x = 12