Question

The denominator of the fraction is 3 more than its numerator and 2is added to the numerator 9is added to the denominator it becomes 5/6then find the orginal fraction​

Answer 1

Solution :-

Let :-

Numerator = x

Denominator = y

According to the first condition :-

$\longrightarrow \sf y = 3+x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..............(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{x+2}{y+9} = \dfrac{5}{6} \\\\\longrightarrow 6(x+2)=5(y+9) \\\\\longrightarrow 6x+12= 5y+45 \\\\\longrightarrow 6x-5y = 33 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

Substitute the value of y in eq(2) :-

$\longrightarrow \sf 6x-5(3+x) = 33 \\\\\longrightarrow 6x-15-5x = 33 \\\\\longrightarrow 6x-5x = 33+15 \\\\\longrightarrow \bf x = 48$

Substitute the value of x in eq(1) :-

$\longrightarrow \sf y = 3+48 \\\\\longrightarrow \bf y = 51$

$\bf FRACTION = \dfrac{48}{51}$