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)
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the denominator of a fraction is 1 less than 4 times the numerator. Denominator becomes 12 times the numerator, if both are reduced
Verified answer
☯GIVEN :
☯TO FIND :
➲SOLUTION :
Let the numerator be x.
Then , denominator = 4x-1
[tex]: \implies{ \sf{12(Num - 3) =Denom - 3 }} \\ \\ [/tex]
[tex]: \implies{ \sf{12(x - 3) =(4x - 1)- 3}} \\ \\ [/tex]
[tex]: \implies{ \sf{12x -36 =4x- 1 - 3}} \\ \\ [/tex]
[tex]: \implies{ \sf{12x -36 =4x - 4 }} \\ \\ [/tex]
[tex]: \implies{ \sf{12x -4x =- 4 + 36}} \\ \\ [/tex]
[tex]: \implies{ \sf{8x =32}} \\ \\ [/tex]
[tex]: \implies{ \sf{x = \cancel{\dfrac{32}{8}}}} \\ \\ [/tex]
[tex]: \implies{ \underline{ \huge{ \pink{\boxed{\bf{x =4}}}}}} [/tex]
★Numerator :
★ Denominator :
[tex]:\longrightarrow {\sf{4x-1}}\\ \\[/tex]
[tex]:\longrightarrow {\sf{4\times 4-1}}\\ \\ [/tex]
[tex]:\longrightarrow {\sf{16-1}}\\ \\ [/tex]
[tex]:\longrightarrow \underline {\boxed {\purple{\bf{15}}}}\\ \\ [/tex]
[tex]\huge {\red{\therefore}}[/tex] Required Fraction is [tex] \bf{\dfrac{4}{15}}[/tex].