Question

a fraction becomes equal to 4 by 5 if 1 is added to both numerator and denominator if however by 5 is subtracted from both numerator and denominator the fraction becomes equal to 1 by 2 what is the fraction

Answer 1

Hey!

Let the fraction be x/y

As given in the question,

*x+1/y+1=4/5
5(x+1)=4(y+1).
5x+5=4y+4.
5x-4y=4-5=-1. (Equation 1)

*x-5/y-5=1/2.
2(x-5)=1(y-5).
2x-10=y-5.
2x-y=-5+10=5. (Equation 2)

Equation 1 × 1 - Equation 2 ×4.
5x-4y=-1.
-8x+4y=-20.
__________
-3x=-21.
x=-21/-3.
=7.
Putting x in equation 2.
2x-y=5.
2*7-y=5.
14-5=y
Y= 9

Therefore the fraction is x/y=7/9.

Hope it helps.

Answer 2

let assume fraction =x/y
if 1 is added, the fraction is x+1/y+1=4/5
5x+5 =4y+4
5x-4y=-1
if 5 is subracted the fraction is x-5/y-5=1/2
2x-10=y-5
2x-y=-5+10
2x-y=5

5x-4y=-1
2x-y=5 (multiply with 4)


5x-4y=-1
8x-4y=20
(_)(+). (_)
-3x= -21
x=-21/-3=7
x=7
substitute x=7 in 2x-y=5
2×7-y=5
14-y=5
-y= 5-14
-y=-9
y=9.
so the fraction is 7/9