Question

Q5. In a rational number, twice the numerator is 2 more than the denominator. If 3
is added to the numerator and the denominator, the newnumber becomes 2/3.​

Answer 1

AnswEr:-

Let the numerator be x

denominator will  be =2x−2

If 3 is added to both then fraction =  2/3

​ ⇒3x+9=4x−4+6

⇒7=x

∴ Denominator =2x−2=12

=>  Fraction =  x/ 2x-2  = 7/12.

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Answer 2

Step-by-step explanation:

$\large\bf\underline\red{Question ➡} \\ \\ \sf in \: a \: rational \: number \: twice \: the \: numerator \: \\ \sf \: is \: 2 \: more \: than \: the \: denominator \: . \\ \sf \: if \: 3 \: is \: added \: to \: the \: numerator \: and \: \\ \sf \: denominator \: the \: number \: becomes \: \frac{2}{3} \\ \sf \: find \: the \:n umber \: ? \\ \\ \large\bf\underline\red{solution➡} \\ \\ \sf \: let \: numerator \: = x \\ \sf \therefore \: denominator \: = 2x - 2 \\ \\ \large\bf\underline\red{A.T.Q} \\\\ \sf \: 3 \: is \: added \: in \: both \: numerator \\ \sf\: and \: denominator \\ \\ \sf \frac{x + 3}{2x - 2 + 3} = \frac{2}{3} \\ \\ \sf \underline{by \: cross \: multiplication} \\ \\\sf \: 3x + 9 = 4x + 2 \\ \\ \sf\fbox\red{ x = 7} \\ \\ \bf \: numerator \: = \fbox\red{ x = 7} \\ \\\sf \: denominator \: = 2x - 2 = 14 - 2 \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 12 \\ \\ \bf \: \: denominator = \fbox\red{ x = 12} \\ \\ \bf \: fraction \: = \: \large{\boxed{\mathfrak\red{\fcolorbox{magenta}{aqua}{7/12}}}}$[/tex]