question_answer

The denominator of a rational number is greater then its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is \[\frac{3}{2}\] . Find the rational number.

Answer:

Let the numerator of rational number be x

and                  denominator = x + 8

Therefore rational number \[=\frac{x}{x+8}\]

According to question,

\[\frac{x+17}{(x+8)-1}=\frac{3}{2}\]

or,      \[\frac{x+17}{x+7}=\frac{3}{2}\]

or,            \[2(x+17)=3(x+7)\]

or,                    \[2x+34=3x+21\]

or      \[2x-3x=21-34\]

[Transposing 3x to LHS and 34 to RHS]

or,                           \[-x\text{ }=-13~~\]

or,                             x = 13

Hence, the required rational number

\[=\frac{13}{13+8}=\frac{13}{21}\]