Question

A fraction becomes 2/3 when it's numerator and denominator are each increased by 2 . however if they are reduced by 1 , the fraction becomes 1/2 .find out the original fraction.​

Answer 1

Answer:

let the numerator be x and denominator be y

therefore the fraction is x/y.

A/Q,

x+2/y+2 =2/3

=>3(x+2)=2(y+2)

=>3x+6=2y+4

=>3x+2=2y

=>3x-2y+2=0-------(i)

Also,

x-1/y-1= 1/2

=>2(x-1)=y-1

=>2x-2=y-1

=>2x-1=y------(ii)

Now, putting value of y in (i) we get,

3x-2(2x-1)+2=0

=>3x-4x+2+2=0

=>-x=-4

=>x=4

Now, putting the value of x in (ii) we get,

2×4-1=y

=>y=7

Therefore the original fraction is x/y=4/7

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