Question

the denominator of a rational number is 1 greater than its numerator if the numerator is increased by 17 and the denominator is decreased by 1 the number becomes 27 find the rational number​

Answer 1

Answer :

›»› The Rational number = 37/11

Given :

• The denominator of a rational number is 1 greater than its numerator If the numerator is increased by 17 and the denominator is decreased by 1 the number becomes.

To Find :

• The rational number = ?

Required Solution :

Here in this question we have to find rational number. So, firstly we have to consider the rational number be a/b, after consider we will find Rational number on the basis of conditions given above.

Let ,

The rational number be a/b

$\tt{: \implies p = q + 1}$

Now ,

The new number will be,

$\tt{: \implies \dfrac{a + 17}{b + 1} = 27}$

$\tt{: \implies \dfrac{a + 17}{b + 2} = 27}$

$\tt{: \implies 27a + 54 = b + 17}$

$\tt{: \implies 26a = - 37}$

$\tt{: \implies a = \dfrac{ - 37}{26} }$

$\tt{: \implies b = \dfrac{ - 11}{26} }$

So ,

$\bf{: \implies \dfrac{a}{b} = \dfrac{37}{11} }$

║Hence, the Rational number is 37/11.║