Question

The denominator of a fraction is 4 more then
twice its numerostor. Denominator becomes 12
times the numerator, if both the numerator
the denominator are reduced by 6 find
the fraction​

Answer 1

☯GIVEN :

• Denominator of a fraction is 4 more than twice its numerator.

• Denominator becomes 12 times the numerator, if both the numerator and the denominator are reduced by 6.

☯TO FIND :

• Required fraction.

➲SOLUTION :

Let the numerator be x.

Then , denominator = 2x+4

• After reducing 6 from both the numerator and the denominator , Denominator becomes 12 times the numerator.

$\implies{ \sf{12(Num - 6) =Denom - 6 }}$

$\implies{ \sf{12(x - 6) =(2x + 4)- 6 }}$

$\implies{ \sf{12x -72 =2x + 4- 6 }}$

$\implies{ \sf{12x -72 =2x - 2 }}$

$\implies{ \sf{12x -2x =- 2 + 72}}$

$\implies{ \sf{10x =70}}$

$\implies{ \sf{x = \cancel{\dfrac{70}{10}}}}$

$\implies{ \underline{ \huge{ \red{\boxed{\bf{x =7}}}}}}$

★Numerator :

• x = 7

★ Denominator :

• Substituting the value of x :

$\longrightarrow {\sf{2x+4}}$

$\longrightarrow {\sf{2\times 7+4}}$

$\longrightarrow {\sf{14+4}}$

$\longrightarrow {\bf{18}}$

$\huge {\pink{\therefore}}$ The original fraction is $\bf{\dfrac{7}{18}}$ .