Question

P. The numerator of a fraction is one-third of the denominator. The numerator
is decreased by 3 and the denominator is increased by 1. Thus the fraction
becomes equal to 1/5. What was the original fraction ?​

Answer 1

SOLUTION :

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.

HOPE THIS WILL HELP YOU...

Answer 2

Fraction is 24/8 or we can write it in simplified form as 3/1...