Question

The denominater of rational number is greater than its numerator by 8. If the denominator is increasedvby 1 and the numerator is increased by 17 the number obtained is 3/2 .Find the original number

Answer 1

this is the answer the no. is 7/15

Answer 2

Answer:

The Original Rational Number is $\frac{7}{15}$

Step-by-step explanation:

Given :

Denominator of the rational number = 8 more than its numerator

When denominator is increased by 1 and the numerator is increased by 17 the number obtained = $\frac{3}{2}$

To find :

The Original Rational Number

Solution :

Let the -

• Numerator be x
• Denominator be (x + 8)

★ $\green{\boxed{\green{\boxed{\red{\sf{ \frac{x + 17}{(x + 8) + 1} = \frac{3}{2}}}}}}}$

$\sf{\longrightarrow}\: \frac{x + 17}{(x + 8) + 1} = \frac{3}{2} \\ \sf{\longrightarrow}\: \frac{x + 17}{x + 9} = \frac{3}{2} \\ \sf{\longrightarrow}\: 2(x + 17) = 3(x + 9) \\ \sf{\longrightarrow}\: 2x + 34 = 3x + 27 \\ \sf{\longrightarrow}\: 3x - 2x = 34 - 27 \\ \sf{\longrightarrow}\: x = 7$

Numerator = 7

$\rule{300}{1.5}$

★ Value of (x + 8)

$\sf{\longrightarrow}\: 7 + 8 \\ \sf{\longrightarrow}\: 15$

• Numerator = 7
• Denominator = 15

Original Number = $\boxed{\boxed{\sf{\frac{7}{15}}}}$

$\therefore$ The Original Rational Number is $\frac{7}{15}$