Question

The denominator of a rational number is greater than its numerator by 6 if the numerator is increased by 5 and the denominator is decreased by 3 the new number becomes 5/4 find the original number

Answer 1

let the numerator be x
therefore denominator be x+6
rational no becomes x/x+6
also when we add 5in numerator and subtract 3 from denominator then the rational no. becomes x+5/(x+6)-3 we get 5/4....given
$x + 5 \div (x + 6) - 3 = 5 \div 4 \\ x + 5 \div (x + 6) = 5 \div 4 \times - 3 \\ x + 5 \div (x + 6) = - 15 \div 4 \\ 4x + 20 = - 15x - 90 \\ 4x + 15x = - 90 - 20 \\ 19x = - 110 \\ x = - 110 \div 19 \\ x = 5.79..$