Question

The numerator of the fraction is 1 more than the denominator.If 5 is subtracted from both the numerator and denominator the fraction becomes 2.Find the number.
to​

Answer 1

$\huge\bf{Answer :}$

The Numerator is $\huge{\boxed{7}}$ And

The Denominator is $\huge{\boxed{6}}$

$\huge\bf{Explanation :}$

Let,

The Numerator be x ,

The Denominator be y .

From Condition 1 ,

$x = y + 1 \\ x - y = 1$

From Condition 2 ,

$\frac{x - 5}{y - 5} = 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ x - 5 = 2(y - 5) \\ x - 5 = 2y - 10 \: \: \\ \: x - 2y = - 10 + 5 \\ x - 2y = - 5 \: \: \: \: \: \: \: \: \:$

Subtract Equation 2 From Equation 1 ,

$\: \: \: \: \: \: x - y = 1 \\ \: - \: \: \: x - 2y = - 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: y = 6$

Put y = 6 in Equation 1 ,

$x - y = 1 \\ x - 6 = 1 \\ x = 1 + 6 \\ x = 7 \: \: \: \: \: \: \: \:$

Hence,

The Numerator is $\huge{\boxed{7}}$ And

The Denominator is $\huge{\boxed{6}}$

$\huge{Thanks}$