Question

The denominator of a rational number is greater than its numerator by 5. If the numeratoris increased by 11 and the denominator is decreased by 14, the new number becomes 5. Find the original rational number.​

Answer 1

Given that,

the denominator of a rational number is greater than it's numerator by 5.

let the numerator of the rational number be x.

therefore it's denominator = x + 5

ATQ,

when the numerator is increased by 11 and the denominator is decreased by 14, then the number becomes 5.

➡ (x + 11)/(x + 5 - 14) = 5

➡ (x + 11)/(x - 9) = 5

➡ x + 11 = 5(x - 9)

➡ x + 11 = 5x - 45

➡ x - 5x = -45 - 11

➡ -4x = -56

➡ x = -56/-4

➡ x = 14

therefore,

numerator = x = 14

denominator = x + 5 = 19

hence, the original number is 14/19.