If both numerator and denominator of a fraction are increased by one, the fraction formed is 2/3. if both numerator and denominator are decreased by two, the fraction formed is 3/5. what is the fraction formed, if both numerator and denominator are increased by four?

Question

Please help me

Answer 1

let the original fraction be x/y

(x+1)/(y+1) = 2/3
3x + 3 = 2y + 2 ----> 3x - 2y = -1 , #1

(x-2)/(y-2) = 3/5
5x - 10 = 3y - 6 ----> 5x - 3y = 4 , #2

#1 times 3 ---> 9x - 6y = -3
#2 times 2 ---> 10x - 6y = 8
subtract them:
x = 11
in #1:
33 - 2y = -1
-2y = -34
y = 17

so the original fraction was 11/17
if both top and bottom are increased by 4 we would have

15/21 or 5/7

Answer 2

Oh God! I made a big mistake at this part

33 - 2y = -1
-2y = 32

I should improve

Answer 3

happens to everybody