Question

the denominator of a rational number is greater than its numerator by 3 in 3 is subtracted from the numerator and 2 is added to the nominal the new number becomes 1 by 5 find the original number check your solution

Answer 1

let n = numerator
n+3 = denominator

n-3/n+3+2 = 1/5

n-3/n+5 = 1/5

5(n-3) = n+5
5n-15 = n+5
4n = 20 

n= 5
n+3 = 8

original no = 5/8

Answer 2

Solution:

Given: The denominator is grater than numerator by 3.
So,Let the numerator be x,
then,the denominator is x+3...     x/(x+3)

when 3 is subtracted from numerator and 2 is added to the denominator,it becomes1/5..
which means,      (x-3)/(x+3+2)=1/5
                                   (x-3)/(x+5)=1/5
                                           5(x-3)=x+5
                                            5x-15=x+5
                                            5x-10=x
                                            5x-x=10
                                              4x=10
                                                x=10/4...numerator is 10/4

                                                x+3=10/4+3
                                                x+3=10/4+12/4
                                                x+3=22/4...... denominator is 22/4
∴The fraction (x/x+3) (10/4/22/4)=>10/22=>5/11