Question

the denominator of a rational number is greater than its numerator by 11 if the numerator is increased by 5 and the denominator is increased by 9 the fraction becomes 2/3. find a rational number

Answer 1

Let the numerator be x
Denominator be y
So fraction = x/y
Given,
y-x = 11.................. (1)
x+5/y+9 = 2/3
3x+15 = 2y+18
3x-2y = - 3.............. (2)
Multiply eq (1) by 2
-2x+2y = 22
Adding (1) and (2)
-2x+2y = 22
3x-2y = - 3
x = 19
put in eq (1)
y-x = 11
y-19 = 11
y = 19+11
= 30
Rational number = 19/30