# A fraction becomes 2/3 if its numerator is increased by 1 and denominator by 2.it becomes 3/4 if its numerator is increased by 4 and the denominator by 5. find the fraction.

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by sam11oscar

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by sam11oscar

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acc to 1st condition;

x+1/y+2=2/3

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

3x+3=2y+4

3x-2y=1---(i)

acc to 2nd condition;

x+4/y+5=3/4

therefore;(x+4)4=(y+5)3

4x+16=3y+15

4x-3y=-1--------(ii)

multiplying (i)by 3 and (ii) by 2 respectively;

9x-6y=3---------(iii)

8x-6y=-2------(iv)

subtracting (iv) from(iii);

9x-6y=3

8x-6y=-2

(-) (+) (-)

----------------

x=5

therfore substituting x=5 in(i)

3(5)-2y=1

15-2y=1

15-1=2y

14=2y

y=7

therfore the fraction is 5/7.

hope i helped u:)