Question

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.

Answer 1

let the fraction be x/y
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:)

Answer 2

the fraction is 5/7..........