Question

if 3 is subtracted from the numerator as well as from the denominator of a fraction if the reduced form of new fractions to obtain is four divide 9 if 3 is added to the numerator as well as the denominator of same fractions the reduced form of new fraction so is to divide 3 find the original fraction

Answer 1

Let original fraction = x/y
given x-3/y-3=4/9 & x+3/y+3=2/3
by cross multiplication equation 1
9x-27 =4y-12=> 9x-4y=15 …………(3)
by cross multiplication equation 2
3x+9=2y+6=> 3x-2y= -3………………(4)
by equation (3) &(4)
9x-4y=15 }×1
3x-2y= -3 }×3
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___________________
-4y+6y= 15+9
=> 2y = 24
=> y = 12
hence from equation (3) , put value of y in equation (3)
=> 9x-4×12=15
=> 9x=15-48
=> x = -3.66
hence original fraction =
-3.66/12