Question

A fraction becomes 1/3 if 2 is added to both numerator and denominato.If 3 is added to both numerator and denominator it becomes 2/5.Find the fraction​

Answer 1

Answer:

let the numerator be x

and denominator be y

then the fraction become x/y

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

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

solving equation (1)

3(x+2)=y+2

3x+4=y____(3)

putting the value of equation (3) in (2) we get

x+3/3x+4+3=2/5

5(x+3)=2(3x+7)

5x+15=6x+14

5x+15-14=6x

5x-6x=-1

-1x= -1

x=1

putting in equation (3) we get

3x+4=y

3+4=y

7=y

y=7

fraction is 1/7

now we check our answer by putting the value of x and y in equation (1) or (2)

x+2/y+2=1/3

1+2/7+2=1/3

3/9=1/3

1/3=1/3

hence ,L.H.S = R.H.S