Question

The denominator of a fraction is greater than the numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2, find the fraction. 

Answer 1

Let p/q is the fraction.
Given : q = p +8 --------eq.1 
When p' = p + 17 , q' = q - 1, we get 
p'/q' = 3/2 = (p+17)/(q-1) 
2(p + 17) = 3(q -1) = 3q - 3 = 2p + 34
3q = 2p + 31 --------------eq.2 
Put eq.1 in 2, we get 
3(p +8 ) = 2p + 31
3p +24 = 2p + 31
p = 7
q = 15
The fraction is 7/15

Answer 2

Given that denominator of a fraction is greater than numerator by 8.

If the numerator is x then the denominator will be x + 8.

Total fraction = x/x+8.   ---- (1)
 
Given that numerator is increased by 17 and decreased by 1, the number is 3/2.


x + 17/x+8-1 = 3/2

x + 17/x + 7 = 3/2

2x + 34 = 3x + 21

x = 13.

Substitute x = 31 in (1), we get

Fraction = 13/21.

Hope this helps!