Question

the denominator of a rational number is less than its ne numerator than 5 if the five is added to the numerator the new number become 11 by 6 find the original number ​

Answer 1

Let the rational number be yx

Given, Denominator of rational number is 4 less than its numerator =>y=x−4=>x−y=4 --- (1)

Also, if 11is added to numerator and 1 is subtracted from denominator the new number,  then number =y−1x+11=37

=>3x+33=7y−7

=>3x−7y=−40 --- (2)

Multiplying equation  (1) with 3 we get, 3x−3y=12 ----- equation (3)

Subtracting equation (3)

from (2), we get 4y=52=>y=13

Substituting y=13 in the

equation (1), we get x=13=4=>x=17

Hence, the number is 1317