Question

twice the numerator is 2 more than the denominator if 3 is added to each the numerator and denominator then a fraction is 2 by 3 find the original number.​

Answer 1

EXPLAINED CLEARLY IN THE PICTURE

HOPE IT HELPS....

PLS MARK AS BRAINLIEST

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Original Fraction is ${\bf{\dfrac{7}{12}}}$

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Twice the numerator = 2 more than the Denominator

3 is added to numerator and Denominator = Fraction is $\tt{\dfrac{2}{3}}$

To Find :

The Original fraction

Solution :

Consider the numerator as x

Denominator = 2x - 2

★ $\green{\boxed{\tt{\red{\frac{x + 3}{(2x - 2) + 3} = \frac{2}{3}}}}}$

$\tt{\implies} \: \dfrac{x + 3}{(2x - 2) + 3} = \dfrac{2}{3}$

$\tt{\implies} \:3(x + 3) = 2(2x - 2 + 3)$

$\tt{\implies} \:3x + 9 = 4x - 4+ 6$

$\tt{\implies} \:3x + 9 = 4x + 2$

$\tt{\implies} \:4x - 3x= 9 - 2$

$\tt{\implies} \:x = 7$

$\rule{300}{1.5}$

★ Value of 2x - 2

$\tt{\implies} \: (7 \times 2) - 2$

$\tt{\implies} \: 14 - 2$

$\tt{\implies} \: 12$

Numerator = 7

Denominator = 12

Fraction = $\boxed{\boxed{\bf{\dfrac{7}{12}}}}$

$\therefore$ The Original Fraction is ${\bf{\dfrac{7}{12}}}$

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

Add 3 to the numerator and Denominator to see whether the new fraction formed is $\tt{\dfrac{2}{3}}$

$\tt{\implies} \: \dfrac{7 + 3}{12 + 3} = \dfrac{2}{3}$

$\tt{\implies} \: \dfrac{10}{15} = \dfrac{2}{3}$

Reduce the Fraction

$\tt{\implies} \: \dfrac{10 \div 5}{15 \div 5} = \dfrac{2}{3}$

$\tt{\implies} \: \dfrac{2}{3} = \dfrac{2}{3}$

$\therefore$ The Original Fraction is ${\bf{\dfrac{7}{12}}}$