Question

In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is - Find the original fraction.

please answer me​

Answer 1

Correct question:-

• In a fraction, twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2/3.

To find:-

• Original Fraction.

Solution:-

Let the numerator of a fraction be x.

Then, Denominator = 2x - 2

Thus, The original Fraction = $\sf \dfrac{x}{2x - 2}$

★ According to question:-

When 3 is added to both numerator and denominator:-

$\dashrightarrow\sf \dfrac{x + 3}{2x - 2 + 3} = \dfrac{2}{3} \\\\ \dashrightarrow\sf \dfrac{x + 3}{2x + 1} = \dfrac{2}{3}$

★ Cross - Multiplication:-

$\dashrightarrow\sf 3(x + 3) = 2(2x + 1)$

$\dashrightarrow\sf 3x + 9 = 4x + 2$

$\dashrightarrow\sf 3x - 4x = 2 - 9$

$\dashrightarrow\sf x = 7$

★ Put the value of x in :-

$\dashrightarrow\sf \dfrac{x}{2x - 2}$

$\dashrightarrow\sf \dfrac{7}{2 \times 7 - 2}$

$\dashrightarrow\sf \dfrac{7}{14 - 2}$

$\dashrightarrow\sf \dfrac{7}{12}$

$\rule{200}3$

Answer 2

Question :-

• In a fraction twice the numerator is 2 more than the denominator. If 3 is added to the numerator and to the denominator the new fraction is 2/3. Find the original number.

AnSwer:-

• Original Fraction is $\dfrac{7}{12}$

ExPlanation:-

$\sf \: Let \: the \: no. \: be \: x$

$\sf \: So \: the \: denominator = 2x-2$

$\sf \: If \: 3 \: is \: added :-$

$\sf \: Numerator= x+3 \\ \sf Denominator= 2x-2+3$

${ \underline{ \bigstar{According \: to \: the \: question, }}}$

$\longmapsto \sf \: 2x+1 \\\longmapsto \sf \: x+3/2x+1=2/3 \\ \longmapsto \sf \:3(x+3)=2(2x+1) \\ \longmapsto \sf \:3x+9=4x+2 \\ \longmapsto \sf \:3x-4x=2-9 \\ \longmapsto \sf \:-x=-7 \\ \longmapsto \sf \:x=7$

$\sf \: Numerator = x = 7 \\ \sf \: Denominator = 2x-2 \\ \\ \implies 2(7)-2 \\ \implies \: 14-2 \\ \implies \: 12 \\ \\ { \blue{\sf {\therefore {\: Original \: Fraction = 7/12}}}}$