Question

the denominator of a rational number is greater than its numerator by7 if 3 is subtracted and 2 is added to its denominator the new number becomes 1/5 find the rational number​

Answer 1

The rational number is $\frac{6}{13}$ .

• Let the numerator of the rational number be x and denominator be y.
• The denominator of rational number is greater than its numerator by 7.

y = x+7       ........(Equation 1)

• Now when 3 is subtracted from the numerator and 2 is added to the denominator then the number becomes $\frac{1}{5}$.

$\frac{x-3}{y+2} = \frac{1}{5}$

5x - 15 = y + 2

y = 5x - 17    .........(Equation 2)

• Equating 1 and 2 , we get

5x - 17 = x + 7

4x = 24

x = 6

• Now substituting the value of x in equation 2 we get,

y = 5(6) - 17

y = 13

• Therefore the rational number becomes $\frac{x}{y}$
• That is $\frac{6}{13}$