Question

if 1 is added to the numerator of a fraction , it becomes 1/5; if 1 is taken from the denominator,it becomes 1/7,find the fraction
in simultaneous equation

Answer 1

Let the numerator be x
Then denominator be y
Then the fraction is x/y
According to problem
(x+1)/y=1/5
5x+5=y-------(1)

x/(y-1)=1/7
7x=y-1
7x+1=y-------(2)
Equating (1) and (2) since R.H.S are equal
5x+5=7x+1
7x-5x=5-1
2x=4
x=2
Substitute x=2 in eq-(1)
(1)=>5(2)+5=y
y=10+5
y=15

Therefore the fraction is 2/15

Answer 2

Let the numerator be 'x' and the denominator be 'y'
Fraction = x/y
(x+1)/y = 1/5                   [According to question]
5x+5 = y                         [Cross Multiplication]
5x-y = -5 ......................... (1)


x/(y-1) = 1/7                   [According to question]
y-1 = 7x                         [Cross Multiplication]
7x-y = -1 ........................ (2)

[Elimination Method]
    5x -  y =     -5
(-)7x(+)y = (+)1              [Symbols of equation change]
---------------------
  -2x        =     -4
x = -4/-2 = 2
Since,
5x-y = -5
y = 5x+5 = 15

Therefore,
Fraction = 2/15