Question

the denominator of a fraction is greater then the numerator by 8 if the numerator is increased by 17 and dinominator is decreased by 1 the number obtained is 3/2 find the fraction​

Answer 1

Answer:

Let the numerator of the fraction be x. Then, denominator = (x + 8).

$\boxed{\sf \star \: Fraction = \dfrac{x}{x + 8}}$

According to the question;

$\sf \implies \frac{x + 17 }{x + 8 - 1} = \frac{3}{2} \\ \\ \sf \implies \frac{x + 17}{x + 7} = \frac{3}{2} \\ \\ \bf on \: cross \: multiplying : \\ \\ \sf \implies 2(x + 17) = 3(x + 7) \\ \\ \sf \implies 2x + 34 = 3x + 21 \\ \\ \sf \implies 3x - 2x = 34 - 21 \\ \\ \sf \implies x = 13$

Now,

$\sf Fraction = \dfrac{x}{x + 8} \\ \\ \sf Fraction = \dfrac{13}{13+ 8} \\ \\ \boxed{ \red{ \bf Fraction = \dfrac{13}{21}}}$

Hence, required answer is 13/21.

Answer 2

Solution :-

Let the Numerator be x.

Denominator = x + 8

Fraction :- $\dfrac{x}{x + 8}$

New Numerator = x + 17

New Denominator = x + 8 - 1

Fraction obtained = $\dfrac{x + 17}{x + 8 - 1}$

According To Question :-

$\sf{\implies}$$\dfrac{x + 17}{x + 8 - 1}$ = $\dfrac{3}{2}$

$\implies$$\dfrac{x + 17}{x + 7}$ = $\dfrac{3}{2}$

$\implies$$2 (x + 17) = 3 (x + 7)$

$\implies$$2x + 34 = 3x + 21$

$\implies$$34 - 21 = 3x - 2x$

$\implies$$x = 13$

So, the Numerator is 13.

Denominator = 13 + 8 = 21

The Fraction is :-

$\implies$$\boxed{\dfrac{13}{21}}$

Hence, the answer is 13/21.