Question

The denominator of a rational number is greater than its numerator by 7. If the numerator is increased by 17 and the denominator decreased by 6, the new number becomes 2. Find the original number.

Answer 1

Let the rational numbers be \(\frac{\text{x}}{y}\)

According to the question 

y = x + 7x = y - 7....(1)

And \(\frac{\text{x + 17}}{y\,-\,6}=2\)

Putting (1), we get,

\(\frac{y\,-\,7\,+\,17}{y\,-\,6}=2\)

By cross multiplication

⇒ y - 7 + 17 = 2(y - 6) 

⇒ y + 10 = 2y - 12 

⇒ 2y - y = 10 + 12 

⇒ y = 22 

⇒ x = y - 7 = 22 - 7 = 15

So the number is \(\frac{15}{22}\)