Question

Numerator of a fraction is 3 less than denominator. If 1 is added to denominator, fraction reduces by 1/15. Find the fraction

Answer 1

Let the denominator of fraction be x
& numerator be x - 3
Fraction = numerator / denominator
Fraction = (x - 3) / x……….(1)
ATQ
x - 3 / x+1 = (x -3 / x ) - 1/15
x - 3 / x+1 = [15 ( x- 3 ) - 1 × x] / 15x
(x - 3 / x +1) =[ 15x - 45 - x] /15x
15x (x-3/x+1) = [ 14x - 45 ]
15x² - 45x = (14x - 45) (x +1)
15x² - 45x = x(14x - 45) + 1 (14x - 45)
15x² - 45x = 14x² - 45x + 14x - 45
15x² - 14x² - 45x + 45x - 14x + 45
x² - 14 x + 45 = 0
x² - 9x - 5x + 45 = 0
[By Middle term splitting]
x(x- 9) - 5(x - 9) = 0
(x - 9) or (x-5)= 0
x= 9 or x = 5
If x = 9
Fraction = (x - 3) / x = (9-3)/9 = 6/9
If x= 5, then
Fraction = (x - 3) / x = (5-3)/5 = ⅖
Hence, the fraction is 6/9 or ⅖.