Question

The denominator of a rational number is greater than the numerator by 6. If the numerator is decreased by 2 and the denominator is increased by 4, the new rational no. obtained is 1/5. Find the original no. ​

Answer 1

$\huge\underline{\red{Answer}}$

Let the numerator be x

Denominator = x + 6

Numerator is decreased by 2

Therefore new Numerator = x - 2

Denominator is increased by 4

Therefore new Denominator = x + 6 + 4

= x + 10

Rational number obtained =

$\frac{x - 2}{x + 10}$

The new Rational number obtained =

$\frac{1}{5}$

According to condition :-

$\frac{x - 2}{x + 10} = \frac{1}{5} \\ = 5(x - 2) = 1(x + 10) \\ = 5x - 10 = x + 10 \\ = 5x - x = 10 + 10 \\ = 4x = 20 \\ = x = \frac{20}{4} \\ = 5$

Therefore numerator = 5

Denominator = x + 6

= 5 + 6

= 11

Original Rational Number =

Original Rational Number =

$\frac{5}{11}$