Question

Hoi ;)
The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2. Find the fraction.​

Answer 1

Step-by-step explanation:

Solution:

Let the numerator of a rational number be $x$

Then, the denominator be $x+8$

Therefore, Rational number = $\frac{x}{x+8}$

According to the question,

⇛ $\frac{x+17}{x+8-1}$ = $\frac{3}{2}$

⇛ $\frac{x+17}{x+7}$ = $\frac{3}{2}$

⇛ 2(x+17) = 3(x+7)

⇛ 2x+34 = 3x+ 21

⇛ 2x-3x = 21-34

⇛ -x = -13

⇛ x = 13

Hence, the required fraction is:

⇛ $\frac{x}{x+8}$

⇛ $\frac{13}{13+8}$

⇛ $\frac{13}{21}$

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