Question

the numerator of a rational number is 3 less than the denominator.if the denominator is increased by 5 and the numerator by 2.we get the rational number of 1/2 find the rational number

Answer 1

let denominator =x
so numerator= x-3
if
(x-3)+2/x+5 =1/2
by cross multiplication
(x-1)2= x+5
2x-2=x+5
2x-x=5+2
x=7
so rational number is x-3/x
= 7-3/7
= 4/7

Answer 2

$let \: the \: denominator \: be \: x \\ so \: numerator = x - 3 \\ fraction = \frac{x - 3}{x} \\ after \: increasing \: the \: denominator \: by \: 5 \: and \: numerator \: by \: 2 \\ fraction = \frac{x - 3 + 2}{x + 5} = \frac{x - 1}{x + 5} \\ according \: to \: question \\ \frac{x - 1}{x + 5} = \frac{1}{2} \\ 2(x - 1) = x + 5 \\ 2x - 2 = x + 5 \\ 2x - x = 5 + 2 \\ x = 7 \\ the \: rational \: no. = \frac{x - 3}{x} = \frac{7 - 3}{7} = \frac{4}{7}$
this is the solution........