Question

If in a rational number denominator is greater than numerator by 8. If you increase the numerator by 17 and decrease the denominator by 1, you get 3/2 as result. Find the number( numerator and denominator)

Answer 1

Answer:

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. ... The rational number will be x/x + 8.

Answer 2

Let :

• numerator = n
• denominator = d

Given :

• d = n + 8

$\bullet \: \sf \dfrac{n + 17}{d - 1} = \dfrac{3}{2}$

To find :

$\sf \: \dfrac{n}{d}$

Solution :

$\sf \dfrac{n + 17}{d - 1} = \dfrac{3}{2} \\ \\ \sf (n + 17) \times 2 = \: 3(d - 1) \\ \\ \sf \: 2n \: + 34 = 3d - 3 \\ \sf \: 2n \: - 3d \: = \: - 3 - 34$

putting value of d in above equation , we get;

$\sf \: 2n \: - 3(n + 8) \: = \: - 37 \\ \sf \: 2n \: - 3n \: - 24 \: = \: - 37 \\ \sf \: - n \: = \: - 37 + 24 \\ \sf \: - n \: = \: - 13 \\ n \: = \: 13 \\ \\ \sf \: therefore \\ \sf d \: = n \: + 8 \: = 13 + 8 \\ \sf d \: = 21$

ANSWER :

$\dfrac{n}{d}=\dfrac{13}{21}$