Question

If2 is added to the numerator of a fraction, it reduces to
1/2 and if 1 is Subtracted from the denominator it
reduces to 1/3.find the fraction.​

Answer 1

$\bf{\Huge{\boxed{\tt{\red{ANSWER\::}}}}}$

$\bf{\Large{\underline{\sf{Given\::}}}}$

If 2 is added to the numerator fraction, it reduces to 1/2 and if 1 is subtracted from the denominator it reduces to 1/3.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

The fraction.

$\bf{\Large{\underline{\rm{\green{Explanation\::}}}}}$

• Let the numerator be R.
• Let the denominator be M.

$\leadsto\tt{\red{The\:fraction\:is\:\frac{R}{M} }}$

$\bf{\Large{\boxed{\rm{First\:\:case}}}}}$

$\longmapsto\sf{\frac{R+2}{M} =\frac{1}{2} }$

$\longmapsto\sf{2(R+2)=1(M)}$

$\longmapsto\sf{2R\:+\:4=M.........................(1)}$

$\bf{\Large{\boxed{\rm{Second\:\:case}}}}}$

$\longmapsto\sf{\frac{R}{M-1} =\frac{1}{3} }$

$\longmapsto\sf{3(R)\:=\:1(M-1)}$

$\longmapsto\sf{3R\:=\:M-1}$

Putting the value of M in above equation, we get;

$\longmapsto\sf{3R=2R+4-1}$

$\longmapsto\sf{3R\:=\:2R+3}$

$\longmapsto\sf{3R\:-\:2R\:=\:3}$

$\longmapsto\sf{\pink{R\:=\:3}}$

Putting the value of R in equation (1), we get;

$\longmapsto\sf{M=2(3)+4}$

$\longmapsto\sf{M\:=\:6+4}$

$\longmapsto\sf{\pink{M\:=\:10}}$

Thus,

$\leadsto\bf{\Large\rm{The\:fraction\:is\:\frac{R}{M} =\frac{3}{10} }}}}$

Answer 2

$\huge\bold\green{AnsWer}$

Acc. tk question we have to find

The fraction.

$\tt{\Large{\orange{Explanation\::}}}$

Let the numerator be = R

Let the denominator be = M

$\sf{The\:fraction\:is\:\frac{R}{M} }$

${\frac{R+2}{M} =\frac{1}{2} }$

${2(R+2)=1(M)}$

$\tt\green{2R\:+\:4=M}$ ___________(¡)

${\frac{R}{M-1} =\frac{1}{3}}$

${3(R)\:=\:1(M-1)}$

${3R\:=\:M-1}$

By substitute the value of M in above equation, we get;

${3R=2R+4-1}$

${3R\:=\:2R+3}$

${3R\:-\:2R\:=\:3}$

$\bold{R\:=\:3}$

Putting the value of R in equation (1), we get;

${M=2(3)+4}$

${M\:=\:6+4}$

$\bold{M\:=\:10}$

Thus, required fraction is

$\frac{R}{M} = \frac{3}{10}$