Question

the denominator of a rational number is greater than its numerator by 8. If the denominator is increased by 1 and the numerator is increased by 17, the number obtained is 3/2 . find the original number.

Answer 1

Answer:

7/15

Step-by-step explanation:

N/(N+8)

(N+17)/(N+9) = 3/2

2N + 34 = 3N +27

N =7

original number = 7/(7+8)

= 7/15

Answer 2

Answer:

$\boxed{\boxed{\boxed{\bold{\sf{\dfrac{7}{15}}}}}}$

Step-by-step explanation:

According to the Question,

$\dfrac{x+17}{x+8+1} = \dfrac{3}{2}\\\\\\\implies \dfrac{x+17}{x+9} = \dfrac{3}{2}\\\\\\\implies 2(x+17) = 3(x+9)\\\\\implies 2x + 34 = 3x + 27\\\\\implies 2x - 3x = 27 - 34\\\\\implies -x = -7\\\\\implies \boxed{x = \boxed{7}}$

$\text{So, the original number is } \dfrac{x}{x+8} = \dfrac{7}{7+8} = \boxed{\boxed{\boxed{\bold{\sf{\dfrac{7}{15}}}}}}$