Question

If 1 is subtracted from numerator and denominator of the rational number then we get 2/5 find the difference of the numerator and denominator if the sum of the numerator and denominator is 9

Answer 1

Answer:

3/9

Step-by-step explanation:

let the numerator be 'x',

then , the denominator will be '9-x',

Now,

A.T.Q

x-1/(9-x)-1 = 2/5

x-1/9-x-1 = 2/5

5(x-1) = 2(9-x-1)

5x-1 = 18-2x-2

7x = 21

x = 3

numerator = 3

& then,

denominator = 9-x = 9-3 = 6

Answer 2

Answer:

let the fraction be x/y

when 1 is subtracted from both numerator and denominator

the fraction become

=(x-1)/(y-1)

and this fraction is equals to 2/5

x-1/y-1=2/5

and in the question sum of numerator and denominator is given 9 so, x+y=9

x=9-y and we will use this in the equation x-1/y-1=2/5

(9-y)-1/y-1=2/5

8-y/y-1=2/5

5(8-y)=2(y-1)

40-5y=2y-2

40+2=2y+5y

42=7y

42/7=y

6=y

and x+y=9 so

x+6=9

x=9-6

x=3

and difference of numerator and denominator is equals to

x-y

3-6=-3

so answer is -3