Question

The denominator of a rational number is greater by 8. If the numerator is increased by 17 and denominator is decreased by 1 the number obtained is 3/2. Find the rational number

Answer 1

Given :

• The denominator of a rational number is greater by 8 of the numerator.
• If the numerator is increased by 17 and denominator is decreased by 1, then the number obtained is 3/2.

To find :

• The rational number.

Solution :

Consider,

• Numerator = x
• Denominator = y

According to the 1st condition :-

• The denominator of a rational number is greater by 8 of the numerator.

$\to\sf{y=x+8...............(i)}$

According to the 2nd condition :-

• If the numerator is increased by 17 and denominator is decreased by 1, then the number obtained is 3/2.

$\to\sf{\dfrac{x+17}{y-1}=\dfrac{3}{2}}$

$\to\sf{\dfrac{x+17}{x+8-1}=\dfrac{3}{2}\:[put\:y=x+8\: from\:eq(1)]}$

$\to\sf{\dfrac{x+17}{x+7}=\dfrac{3}{2}}$

$\to\sf{3x+21=2x+34}$

$\to\sf{3x-2x=34-21}$

$\to\sf{x=13}$

• Numerator = 13

Now, put x = 13 in eq(1) for getting the value of x.

$\to\sf{y=x+8}$

$\to\sf{y=13+8}$

$\to\sf{y=21}$

• Denominator = 21

Therefore,

${\boxed{\large{\bold{Rational\: number=\dfrac{13}{21}}}}}$