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
Answers
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:
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