Question

if 1 is added to each of the two numbers their becomes 1:2 and when 5 is subtracted from each of these the ratio becomes 5:11.find the number​

Answer 1

Answer:

Let the denominator be y

Let the numerator be x

When 1 id added to both of them,

x+1/y+1=1/2

Cross multiply,

2(x+1)=1(y+1)

2x+2=y+1

2x-y=-1                                               equation 1

When 5 is subtracted from each of them,

x-5/y-5=5/11

11(x-5)=5(y-5)

11x-55=5y-25

11x-5y=30                                          equation 2

By eliminating method,

Multipying eq 1 by 5(so to make the coefficient of y equal thus eliminating it),

11x-5y=30

10x-5y=-5

-     +     +

x=35

Now substituting value of x in eq 1,

2(35)-y=-1

-y=-1-70

-y=-71

y=71

Therefore, x=35, y=71