Question

6) The numerator of a fraction is 3 less than the denominator. If 2 is added to the numerator
and 4 is added to the denominator the resulting fraction becomes 2/3. Find the fraction.
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Answer 1

Let the fraction be $\frac{x}{y}$

According to the comdotions ;

x = y - 3 ----(1)

$\frac{x + 2 }{y + 4} = \frac{2}{3} \\ 3x + 6 = 2y + 8$ ----(2)

substituting eq (1) in eq (2)

3y - 3 + 6 = 2y + 8

y = 8 - 3

y = 5

substituting y = 5 in eq (1)

x = 5 - 3

x = 2

Therefore the fraction is

$\frac{2}{5}$

Answer 2

Step-by-step explanation:

Let the denominator to be x.

Original fraction = $\frac{x-3} {x}$

According to the question,

$\frac{(x - 3) + 2}{x + 4} = \frac{2}{3} \\ \frac{x - 3 + 2}{x + 4} = \frac{2}{3} \\ \frac{x - 1}{x + 4} = \frac{2}{3} \\ 3(x - 1) = 2(x + 4) \\ 3x - 3 = 2x + 8 \\ 3x - 2x = 3 + 8 \\ x = 11 \\ \\ \\ So\\ \: \boxed{original \: fraction \: = \frac{x - 3}{x} = \frac{11 - 3}{11} = \frac{8}{11}}$