Question

The numerator of a fraction is 8 less than its denominator. If 2 is added to both numerator and denominator, fraction becomes Find the fraction. ​

Answer 1

★ Cᴏɴᴄᴇᴘᴛ :

Here we need to assume the value of a numerator and then 8 will be added to the denominator as given in the question. Now, 2 is added to both the numerator as well as the denominator. The new fraction is 11/19 which will be in the other side of the equation. We need to find the original fraction.

______________________________

Let us assume that the numerator be a

The denominator will be a + 8

$\star \quad \underline{ \boxed{\frak{ \pink{Original \: Fraction} = \blue{ \frac {Numerator}{Denominator}}}}}$

$\implies \frak{Original \: Fraction = \frac{a}{a + 8} }$

Now, 2 is added to both the numerator and denominator

$\rightarrow \frak{Fraction = \frac{a + 2}{a + 8 + 2}}$

$\rightarrow \frak{Fraction = \frac{a + 2}{a + 10}}$

After which the new fraction becomes 11/19

So, the original fraction = the new fraction

$\frak{Original \: Fraction = New \: Fraction }$

$\frak{ \frac{a + 2}{a + 10} = \frac{11}{19} }$

Cross multiplying..

$\frak{19(a + 2) = 11(a + 10)}$

$\frak{19a + 38 = 11a + 110}$

$\frak{19a - 11a = 110 - 38 }$

$\frak{8a = 72}$

$\star \quad \frak{ \green{a = 9}}$

Now, finding original fraction by putting a's value

$\rightharpoonup \frak{Original \: Fraction = \frac{a}{a + 8} }$

$\rightharpoonup \frak{Original \: Fraction = \frac{9}{9 + 8} }$

$\rightharpoonup \frak{Original \: Fraction = \frac{9}{17} }$

• Hence, the Oʀɪɢɪɴᴀʟ Fʀᴀᴄᴛɪᴏɴ is 9/17

Answer 2

Correct Question:

The denominator of a fraction is 8 less than its denominator if 2 is added to both numerator and denominator section become 11 upon 19 find the fraction

Given:-

† The numerator of a fraction is 8 less than its denominator.

† If 2 is added to both numerator as well as denominator the fraction becomes 11 upon 19.

To Find:-

† What's the Fraction?

Solution :-

$\sf \underline {Let}$

The denominator of the fraction be x.It’s given that the numerator of a fraction is 8 less than its denominator. So, its numerator will be (x - 8) and the fraction will be (x-8)/x.

★ According to the question

$\sf \::\implies \dfrac{(x - 8) + 2}{x + 2} = \dfrac{11}{19}$

$\sf :\implies\dfrac{x - 8 + 2}{x + 2} = \dfrac{11}{19}$

$\sf :\implies\dfrac{x - 6}{x + 2} = \dfrac{11}{19}$

$\sf :\implies 19(x - 6) = 11(x + 2)$

$\sf :\implies 19x - 114 = 11x + 22$

$\sf :\implies 19x - 11x = 22 + 114$

$\sf :\implies 8x = 136$

$\sf :\implies x = \cancel\dfrac{136}{8}$

$\sf :\implies{\underline{\boxed{\frak{\pink{x =17}}}}}\:\bigstar$

$\therefore\:\underline{\textsf{The Denominator is \textbf{17}}}.$

$\dag\underline{\sf{\sf The\: \: of \:Numerator \: of the\: fraction\: is :- }}$

$\sf:\implies x - 8 = 17 - 8.$

$\sf:\implies \boxed{ \sf Numerator = 9.}$

$\therefore\:\underline{\textsf{The fraction will be \textbf{9/17}}}.$