Question

the denominator of a rational number is greater than numerator by 8. if the number is increased by 17 & denominator is decreased by 1, the number obtained is 9/4. find the rational number​

Answer 1

Answer:

13/21, just take numerator as x and denominator as x+8

Answer 2

• The rational number = $\sf \dfrac{1}{9}.$

Given :

• The denominator of a rational number is greater than the numerator by 8.
• The numerator is increased by 17.
• The denominator is decreased by 1.
• The number obtained after increasing the numerator and decreasing the denominator = $\sf \dfrac{9}{4}$

To Find :

• The rational number.

Solution :

Let,

The numerator be x.

The denominator be x + 8 because according to the question, the denominator of a rational number is greater than the numerator by 8.

According to the condition,

The numerator is increased by 17 and the denominator is decreased by 1, the number obtained is $\sf \dfrac{9}{4}.$

$: \implies \rm \dfrac{x + 17}{x + 8 - 1 } = \dfrac{9}{4} \: \: \: ......(1)\\ \\ : \implies \rm \dfrac{x + 17}{x + 7} = \dfrac{9}{4} \\ \\ : \implies \rm 9(x + 7) = 4(x + 17) \\ \\ : \implies \rm 9x + 63 = 4x + 68 \\ \\ : \implies \rm 9x - 4x = 68 - 63 \\ \\ : \implies \rm 5x = 5 \\ \\ : \implies \rm x = \dfrac{ \not5}{ \not5} \\ \\ : \implies \rm x = 1 \\ \\ \: \: \rm \therefore \: \: x = 1$

So, the denominator and the numerator of a rational number are :

★ The numerator = x = 1

★ The denominator = x + 8 = 1 + 8 = 9

Hence,

The rational number is $\sf \dfrac{1}{9}.$

Verification :

Substitute the value of the numerator and the denominator in equation (1),

• Value of the numerator (x) = 1.
• Value of the denominator (x + 8) = 9.

$: \implies \rm \dfrac{x + 17}{x + 8 - 1} = \frac{9}{4} \\ \\ : \implies \rm \dfrac{1 + 17}{9 - 1} = \dfrac{9}{4} \\ \\ : \implies \rm \dfrac{ \not{18}}{ \not{8}} = \dfrac{9}{4} \\ \\ : \implies \rm \frac{9}{4} = \frac{9}{4}$

Hence Verified !