Question

The denominator of a ratio' al number is greater than its numerator by 8. If the
numerator is increased by 17 and the denominator is decreased by 1, the number
obtained is . Find the rational number.​

Answer 1

Step-by-step explanation:

which is required ans of this question

Answer 2

Let the numerator be x then the denominator = x + 8.

$\therefore \tt \: Required \: rational \: no. = \tt \purple{ \frac{x}{x + 18} }$

$\tt \: New \: rational \: no.= \red{\frac{Numerator + 17}{Denominator - 1} }$

$\rightarrow \: \frac{x + 17}{(x + 8) - 1} = \frac{x + 17}{x + 7}$

It is given that new rational number = 3/2.

$\therefore \tt \: \frac{x + 17}{x + 7} = \frac{3}{2}$

$\rightarrow \tt \: 2(x + 17) = 3(x + 7)$

$\rightarrow \tt \: 2x + 34 = 3x + 21$

$\rightarrow \tt \: 2x - 3x = 21 - 34$

$\rightarrow \tt \: - x = - 13$

$\rightarrow \: x = 13$

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$\therefore \tt \: Required \: rational \: no. = \frac{x}{x + 8}$

$= \frac{13}{13 + 8}$

$= \bold { \frac{13}{12} }$