Question

A rational number has its denominator greater than its numerator by 6. If the numerator is increased by 4 and the denominator is decreased by 8, the number becomes 5/3. What is the original rational number ?

1. 11/17
2. 5/17
3. 7/13
4. 13/19

Answer 1

Correct Answer - Option 1 : 11/17

Concept used:

The numerator is the upper part and denominator is the lower part of any fraction

Calculation:

Let the numerator of the rational number be x then its denominator be x + 6

Rational number = Numerator/Denominator

The original rational number = x/(x + 6)

Now, A/Q

(x + 4)/(x + 6 – 8) = 5/3

⇒ (x + 4)/(x – 2) = 5/3

⇒ 3(x + 4) = 5(x – 2)

⇒ 3x + 12 = 5x – 10

⇒ 2x = 22

⇒ x = 11

Numerator = x and Denominator = 11 + 6 = 17

∴ The original rational number is 11/17