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

Answer 1

Answer:

13/21

Step-by-step explanation:

Answer 2

Given :

• 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.

To find :

• The rational number.

Solution :

Consider,

• Numerator = m
• Denominator = n

${\underline{\sf{According\:to\:the\:1st\: condition:-}}}$

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

$\to\sf{n=m+8................(i)}$

${\underline{\sf{According\:to\:the\:2nd\: condition:-}}}$

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

$\to\sf{\dfrac{m+17}{n-1}=\dfrac{3}{2}}$

$\to\sf{\dfrac{m+17}{m+8-1}=\dfrac{3}{2}\:[Put\:n=m+8\: from\:eq(i)]}$

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

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

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

$\to\sf{m=13}$

• Numerator = 13

Now , put m = 13 in eq(i) for getting the value of n.

$\to\sf{n=m+8}$

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

$\to\sf{n=21}$

• Denominator = 21

Therefore,

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