Question

a fraction reduces by 4/ 5 when 6 is subtracted to the denominator but it reduces 12/7 if 6 is added to numerator and denominator is multiplied by 2 find the fraction

Answer 1

let the numerator be x and denominator be y.
x/y-6 = 4/5 (a)
x+6/2y = 12/7 (b)

5x = 4y - 24 => 5x - 4y= -24
7x + 42 = 24y => 7x - 24y = -42

x = (4y - 24)/5
7(4y - 24) - 24y = -42
28y - 168 - 24y = -42
4y = 168-42
y = 126/4

y = 63/2

x = 4(63/2)-24/5
x = 63 x 2 /5
x = 126/5

x/y = (126/5)/(63/2)
x/y = 126 x 2/63 x 5
x/y = 252/315
x/y = 7(36)/7(45)
x/y = 36/45