Question

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

Answer 1

Answer:

Let the numerator be x

denominator will = 2 x − 2

If 3 is added to both then fraction = 3 2

⇒ 2 x − 2 + 3 x + 3 = 32

⇒ 3 x + 9 = 4 x − 4 + 6

⇒ 7 = x

∴ Denominator =2x−2=12

Fraction =2x−2x=127.

Answer 2

Answer:

Appropriate Question :-

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

Given :-

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

To Find :-

• What is the original fraction.

Solution :-

Let,

$\mapsto \bf Numerator =\: x$

$\mapsto \bf Denominator =\: 2x - 2$

Hence, the original fraction will be :

$\leadsto \sf Original\: Fraction =\: \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\pink{Original\: Fraction =\: \dfrac{x}{2x - 2}}}$

According to the question,

$\bigstar$ 3 is added to the numerator and denominator, the new fraction is 2/3.

$\implies \bf \dfrac{Numerator + 3}{Denominator + 3} =\: New\: Fraction$

$\implies \sf \dfrac{x + 3}{2x - 2 + 3} =\: \dfrac{2}{3}$

$\implies \sf \dfrac{x + 3}{2x + 1} =\: \dfrac{2}{3}$

By doing cross multiplication we get,

$\implies \sf 2(2x + 1) =\: 3(x + 3)$

$\implies \sf 4x + 2 =\: 3x + 9$

$\implies \sf 4x - 3x =\: 9 - 2$

$\implies \sf\bold{\purple{x =\: 7}}$

Hence, the required original fraction is :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x}{2x - 2}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7}{2(7) - 2}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7}{14 - 2}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{7}{12}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{7}{12}\: .}}}}$