Question

world problem in maths 1 question the denominator of a rational number is grater than its numerator by 8, if the numerator is increased by17 and the denominator is increased by, 1 the number obtained is 3 by 2. find the rational number​

Answer 1

Let the numerator be x

So, denominator be x + 8

We know

$\red{ \rm Fraction = \dfrac{Numerator}{Denominator}}$

So,

$\rm \dfrac{x}{x+8}$

So, we get the fraction

$\bf \dfrac{x}{x+8}$

Now according to question

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

→ $\sf 2(x+1) = 3(x+7)$

→ $\sf \dfrac{x+1}{x+7} = \dfrac{3}{2}$

→ $\sf 2x+2 = 3x+21$

→ $\sf -x = 19$

So, we got the value of x which is -19

So, simply subsituting in our fraction

$\rm \dfrac{x}{x+8}$

$\implies \sf \dfrac{-19}{-19+8}$

$\implies \sf \dfrac{-19}{-11}$

So, finally we got the fraction which is :-

$\green{\underbrace{\boxed{\overbrace{\dfrac{-19}{-11}}}}}$