Question

15. The deno
The denominator of a rational number is greater than its
numerator by 8. If the denominator is
increased by 1 and the numerator is increased by 17, the number, the number obtained is 3/2
.. Find the
original number,​

Answer 1

Answer:

Original Number = $\frac{7}{15}$ .

Step-by-step explanation:

Let original numerator be x and original denominator be y.

First condition says that denominator of a rational number is greater than its  numerator by 8 i.e.,

                        $y$ = $x$ + 8   ------------ [Equation 1]

Second condition says that if the denominator is  increased by 1 and the numerator is increased by 17, the number obtained is 3/2 i.e.,

               ⇒ $\frac{x+17}{y+1} = \frac{3}{2}$  --------------- [Equation 2]

Now, putting value of y from equation 1 into equation 2 we get,

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

               ⇒ 2($x$ + 17) = 3($x$ + 9)

               ⇒  2$x$ + 34 = 3$x$ + 27

               ⇒  3$x$ - 2$x$ = 34 - 27   ⇒ $x$ = 7

And putting value of x in equation 1 we get, $y$ = 7 + 8 = 15.

Hence, the original number = $\frac{x}{y}$ = $\frac{7}{15}$ .