Question

the denominator of the fraction is greater than the numerator by 9 if the numerator is increased by 17 and denominator is decreased by 1 the number obtained is 3/2 find the fraction ​

Answer 1

Answer:

10/19

Step-by-step explanation:

let the numerator = x

so, denominator = x+9

according to the question,

x/(x+9) is the fraction

and

(x + 17)/(x+8) = 3/2

by cross multiplication,

2(x + 17) = 3(x+8)

2x + 34 = 3x + 24

3x - 2x = 34- 24

x = 10

so fraction is x/(x+9) = 10/19

Answer 2

✪ $\huge{\red{\underline{\overline{\mathbf{Question}}}}}$ ✪

→the denominator of the fraction is greater than the numerator by 9 if the numerator is increased by 17 and denominator is decreased by 1 the number obtained is 3/2 find the fraction

✪ $\huge{\green{\underline{\overline{\mathbf{Answer}}}}}$ ✪

⇒Given:

• Denominator is 9 greater than Numerator

⇒To Find:

• The original Fraction

⇒Solution:

⇒Let The Numerator be x

$\therefore$ The denominator is x+9

Fraction is :-

$\huge{\frac{x}{x+9}}$

According to question-

⇒$\frac{x+17}{x+9-1}=\frac{3}{2}$

⇒$\frac{x+17}{x+8}=\frac{3}{2}$

⇒$2(x+17)=3(x+8)$ {Cross multiplication}

⇒$2x+34=3x+24$

⇒$3x-2x=34-24$

⇒$x=10$

This value of x is Numerator

Denominator = x + 9

⇒$Denominator=19$

Original Fraction is-

⇒$\huge{\pink{\overbrace{\underbrace{\frac{10}{19}}}}}$

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