Question

in a friction, twice the numerator
is 2 more than the denominator.
If 3 is added to the mumerator
and to the denominator, the
mew fraction is 2by3. For the
original fraction​

Answer 1

Answer:

Let the Numerator be a and Denominator will be (2a - 2) respectively.

$\underline{\bigstar\:\:\textsf{According to the Question :}}$

$\dashrightarrow\tt\:\:\dfrac{Numerator+3}{Denominator+3}=\dfrac{2}{3}\\\\\\\dashrightarrow\tt\:\:\dfrac{a+3}{(2a - 2)+3}=\dfrac{2}{3}\\\\\\\dashrightarrow\tt\:\:\dfrac{a + 3}{2a + 1} = \dfrac{2}{3}\\\\\\\dashrightarrow\tt\:\:3(a + 3) = 2(2a + 1)\\\\\\\dashrightarrow\tt\:\:3a + 9=4a + 2\\\\\\\dashrightarrow\tt\:\:9 - 2 = 4a -3a\\\\\\\dashrightarrow\tt\:\:a = 7$

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$\underline{\bigstar\:\:\textsf{Original Fraction :}}$

$:\implies\tt Fraction=\dfrac{Numerator}{Denominator}\\\\\\:\implies\tt Fraction=\dfrac{a}{(2a-2)}\\\\\\:\implies\tt Fraction = \dfrac{7}{2(7) - 2}\\\\\\:\implies\tt Fraction = \dfrac{7}{14 - 2}\\\\\\:\implies\underline{\boxed{\tt Fraction = \dfrac{7}{12}}}$

Answer 2

Answer:-

Original fraction = 7/12

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Solution:-

Case l —

• Twice the numerator is 2 more than the denominator.

Let the numerator be N & denominator be D

A/q,

→ 2N = D + 2

→ N = (D + 2)/2 ---------- Equation (1)

Case 2 —

• 3 added to numerator & denominator new fraction 2/3

A/q,

→ (N + 3)/(D + 3) = 2/3

→ 3(N + 3) = 2(D + 3)

→ 3N + 9 = 2D + 6

→ 3N = 2D + 6 - 9

→ 3N = 2D - 3

→N = (2D - 3)/3 --------- Equation (2)

Comparing both equations:-

→ (D + 2)/2 = (2D - 3)/3

→ 3(D + 2) = 2(2D - 3)

→ 3D + 6 = 4D - 6

→ 4D - 3D = 6 + 6

→ D = 12

∴ Denominator = 12

Now put value in (Equation) 1:-

→ N = (12 + 2)/2

→ N = 14/2

→ N = 7

∴ Numerator = 7

Now fraction:-

→ Original fraction = N/D

→ Original fraction = 7/12

Therefore,

$\therefore\underline{\boxed{\textsf{Original fraction = {\textbf{ \dfrac{7}{12} }}}}}$