Question

The denominator of a rational 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 32. Find the rational number.

Answer 1

CORRECT QUESTION :-

The denominator of a rational 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  3 / 2. Find the rational number.

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow \sf y= x+8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+17}{y-1}=\dfrac{3}{2}\\\\\longrightarrow 2(x+17)= 3(y-1)\\\\\longrightarrow 2x+34= 3y-3 \\\\\longrightarrow 2x-3y = -37\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

Substitute the value of y in eq(2),

$\longrightarrow\sf 2x-3(x+8)= -37 \\\\\longrightarrow 2x-3x-24 = -37\\\\\longrightarrow -x = -13 \\\\\longrightarrow\bf x = 13$

Numerator = 13

Denominator = 13 + 8 = 21

$\bf FRACTION = \dfrac{13}{21}$