Question

When one is added to the numerator as well as the denominator of a certain fraction,it becomes 1/2 and if one is subtracted from the numerator and denominator both, the fraction becomes 1/3 find. The original fraction​

Answer 1

answer:-

answer is 3/7

solution:-

Let the numerator and denominator of the fraction be x and y.Then the fraction will be x/y.

if 1 is subtracted from both numerator and denominator ,the fraction becomes 1/3.thus we have

x-1/y-1=1/3

3 (x-1)=y-1

3x-y-2=0

if 1 is added to both numerator and denominator , the fraction becomes 1/2.thus we have

x+1/y+1=1/2

2 (x+1)=y+1

2x+2=y+1

2x-y+1=0

So we have 2 equations

3x-y-2=0

2x-y+1=0

here x and y are unknowns

We have to solve the above equation for x and y

By using cross multiplication we have

x

---------------------=

(-1)×1-(-1)×(-2)

-y 1

-----------------------=-------------------------

3×1-2×2 (-2)) 3×(-1)-2×(-1)

x -y 1

----=--------=---------------

-3 3+4 -3+2

× -y 1

----=--------=------------

-3 7 -1

x y

----=----------=1

3 7

x=3,y=7

hence the fraction is 3/7