Question

a fraction bexome 8/11, if 3is added to both the numerator and the denominator also if 3 is. substracted from the numerator and the denominator it become 2/5 . find the fraction​

Answer 1

AnswEr :

Let the Numerator and Denominator of the Original Fraction be n and, d.

$\maltese\:\boxed{\tt Original\: Fraction=\dfrac{n}{d}}$

$\rule{100}{2}$

$\underline{\bigstar\:\textsf{According to the First Part :}}$

$\twoheadrightarrow\tt\:\:\dfrac{n+3}{d+3}=\dfrac{8}{11}\\\\\\\twoheadrightarrow\tt\:\:(n + 3)11 = 8(d + 3)\\\\\\\twoheadrightarrow\tt\:\:11n + 33 = 8d + 24\\\\\\\twoheadrightarrow\tt\:\:11n - 8d = 24 - 33\\\\\\\twoheadrightarrow\tt\:\:11n - 8d = - 9 \qquad \dfrac{\quad}{}eq.(1)$

$\underline{\bigstar\:\textsf{According to the Second Part :}}$

$\twoheadrightarrow\tt\:\:\dfrac{n-3}{d-3}=\dfrac{2}{5}\\\\\\\twoheadrightarrow\tt\:\:(n - 3)5= 2(d - 3)\\\\\\\twoheadrightarrow\tt\:\:5n -15=2d -6\\\\\\\twoheadrightarrow\tt\:\:5n -2d = 15 - 6\\\\\\\twoheadrightarrow\tt\:\:5n - 2d =9 \qquad \dfrac{\quad}{}eq.(2)$

$\rule{200}{1}$

$\underline{\bigstar\:\textsf{Multiplying eq.(2) by 4 and subtracting eq.(1) from it :}}$

$:\implies\tt 20n - 8d = 36\\\\:\implies\tt 11n -8d = -9\\\dfrac{\qquad\qquad\qquad\qquad\qquad}{}\\:\implies\tt (20n - 11n) = (36 - (-9))\\\\\\:\implies\tt 9n = 45\\\\\\:\implies\tt n = \dfrac{45}{9}\\\\\\:\implies\red{\tt n = 5}$

$\underline{\bigstar\:\textsf{Putting the value of n in eq.(2) :}}$

$:\implies\tt 5n - 2d = 9\\\\\\:\implies\tt 5(5) - 2d = 9\\\\\\:\implies\tt 25 - 2d = 9\\\\\\:\implies\tt 25 -9 = 2d\\\\\\:\implies\tt 16=2d\\\\\\:\implies\tt \dfrac{16}{2}=d\\\\\\:\implies\red{\tt d = 8}$

$\rule{170}{2}$

$\therefore\:\large \underline{\boxed{\tt Original\: Fraction=\dfrac{n}{d}=\dfrac{5}{8}}}$

Answer 2

Answer:

⇒ x + 3 /y + 3 = 8 /11

⇒ 11x + 33 = 8y + 24

⇒ 8y - 11x = 9....(1)

⇒ x - 3 /y - 3 = 2 /5

⇒ 5x - 15 = 2y - 6

⇒ 5x - 2y = 9...(2)

• Solving (1) and (2) multiply (2) with 4 :

⇒ 8y - 11x = 9

⇒ 20x - 8y = 36

_________________

⇒ 9x = 45

⇒ x = 5

⇒ y = 8

∴ x /y = 5 /8