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:

$\large\boxed{\sf{\dfrac{13}{21}}}$

Step-by-step explanation:

Let the numerator be x.

Therefore, the denominator will be (x+8)

Therefore, the required fraction is x/(x+8)

Now, according to question,

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

Therefore, we will get,

$= > \dfrac{x + 17}{(x + 8) - 1} = \dfrac{3}{2}$

Doing cross multiplication, we get,

$= > 2(x + 17) = 3(x + 8 - 1) \\ \\ = > 2x + 34 = 3x + 24 - 3 \\ \\ = > 3x - 2x = 34 - 24 + 3 \\ \\ = > x = 10 + 3 \\ \\ = > x = 13$

Therefore, we will get,

=> x + 8 = 13+8 = 21

Hence, the required real number is 13/21.