Question

The denominator of a rational number greater than its numerator by 3.If the numerator is increased by 16 and the denominator is decreased by 1,then the number obtained by.Find the rational number.

Answer 1

Step-by-step explanation:

Let the numerator be x then denominator will be (x + 8).

According to the question,

\begin{array}{l} \frac{(x+17)}{(x+8-1)}=\frac{3}{2} \\ \Rightarrow \frac{(x+17)}{(x+7)}=\frac{3}{2} \end{array}

(x+8−1)

(x+17)

=

2

3

⇒

(x+7)

(x+17)

=

2

3

⇒ 2(x + 17) = 3(x + 7)

⇒ 2x + 34 = 3x + 21

⇒ 34 - 21 = 3x - 2x

⇒ 13 = x

The rational number is \frac{x}{x+8}=\frac{13}{21}

x+8

x

=

21

13