Question

the denominator of a fraction is 1 less than 4 times the numerator. Denominator becomes 12 times the numerator, if both are reduced by 3. find the fraction( give the solution as well)​

Answer 1

☯GIVEN :

• The denominator of a fraction is 1 less than 4 times the numerator.

• Denominator becomes 12 times the numerator if both the numerator and the denominator are reduced by 3.

☯TO FIND :

• Required Fraction.

➲SOLUTION :

Let the numerator be x.

Then , denominator = 4x-1

• After reducing 3 from both the numerator and the denominator, the Denominator becomes 12 times the numerator.

$: \implies{ \sf{12(Num - 3) =Denom - 3 }}$

$: \implies{ \sf{12(x - 3) =(4x - 1)- 3}}$

$: \implies{ \sf{12x -36 =4x- 1 - 3}}$

$: \implies{ \sf{12x -36 =4x - 4 }}$

$: \implies{ \sf{12x -4x =- 4 + 36}}$

$: \implies{ \sf{8x =32}}$

$: \implies{ \sf{x = \cancel{\dfrac{32}{8}}}}$

$: \implies{ \underline{ \huge{ \pink{\boxed{\bf{x =4}}}}}}$

★Numerator :

• $\bf{x = 4}$

★ Denominator :

• Substituting the value of x :

$:\longrightarrow {\sf{4x-1}}$

$:\longrightarrow {\sf{4\times 4-1}}$

$:\longrightarrow {\sf{16-1}}$

$:\longrightarrow \underline {\boxed {\purple{\bf{15}}}}$

$\huge {\red{\therefore}}$ Required Fraction is $\bf{\dfrac{4}{15}}$.