Question

the denominator of a number rational number exceed its numerator by 6.if 1 is subtracted from the numerator as well as denominator ,the value of new original number is 1 devided by 2.find the origional number

Answer 1

Hey,
Let the numerator and the denominator be X and y respectively,
So, y-x=6(1st equation)
Now, second equation is,
x-1/y-1=1/2
on cross multiplication,
2(x-1)=1(y-1)
2x-2=y-1
2x-y=1

Solve the two equations,
In first equation,
y-x=6
y=6+x
So, substitute y's value to equation second,
2x-(6+x)=1
2x-6-x=1
x-6=1
x=7.

So, y=6+x
y=6+7
y=13.

So,The original number is x/y=7/13.

Hope this helps you buddy !!
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