Question

A fraction becomes 1/3 ,if 2 is added to both of its numerator and denominator .If 3 is added to both of its numerator and denominator then it becomes 2/5.Find the fraction.

Answer 1

Step-by-step explanation:

let the fraction is x/y

if 2 added to both of its numerator and denominator then

(x+2)/(y+2)=1/3

or, 3x+6=y+2

or, 3x-y=-4....(i)

and if 3 added to both of its numerator and denominator

then

(x+3)/+(y+3)=2/5

5x+15=2y+6

5x-2y=-9(ii)

solving equations i and ii

3x-y=-4...×(2)

5x-2y=-9... ×(1)

___________

6x-2y=-8

5x-2y=-9

- + +

________

x=1

and 6x-2y=-8

6-2y=-8

-2y=-14

y=7

so the fraction of question is (1/7)