Question

A person sells a table at a profit of 10%.If he have brought the table at 5% less cost sold for 80 more.He would have gained 20%.what is the cost price of table​

Answer 1

AnswEr :

Rs.2000.

$\bf{\orange{\underline{\underline{\bf{Given\::}}}}}$

A person sells a table at a profit of 10%. If he have brought the table at 5% less cost sold for 80 more. He would have gained 20%.

$\bf{\grey{\underline{\underline{\bf{To\:find\::}}}}}$

The cost price of table.

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

Let the Cost price (C.P.) be Rs.r

Formula use :

$\bf{\small{\boxed{\bf{Selling\:price\:(S.P.)=\frac{100+profit\%}{100}\times C.P. }}}}}$

$\star$A person sells a table at a profit of 10% :

$\mapsto\sf{S.P.=\dfrac{100+10}{100} \times r}\\\\\\\mapsto\sf{S.P.=\dfrac{11\cancel{0}}{10\cancel{0}} \times r}\\\\\\\mapsto\sf{\red{S.P.=\dfrac{11r}{10} }}$

$\star$Cost price of the table 10 % loss :

$\bf{\small{\boxed{\bf{Selling\:price\:(S.P.)=\frac{100-loss\%}{100}\times C.P. }}}}}$

$\mapsto\sf{S.P.=\dfrac{100-5}{100} \times r}\\\\\\\mapsto\sf{S.P.=\cancel{\dfrac{95}{100}} \times r}\\\\\\\mapsto\sf{\red{S.P.=\dfrac{19r}{20} }}$

Now;

$\leadsto\sf{Selling\:price\:of\:table\:=\dfrac{11r}{10} +80}}$

$\bf{\small{\boxed{\bf{Profit\:(\%)=\frac{profit\times 100}{C.P.}\times 100 }}}}}$

$\mapsto\sf{20\%=\dfrac{S.P.-C.P.}{C.P.} }\\\\\\\mapsto\sf{\dfrac{20}{100} =\dfrac{\frac{11r}{10}+80-\frac{19r}{20} }{\frac{19r}{20} } }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{\frac{22r+1600-19r}{20} }{\frac{19r}{20} } }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{\frac{3r+1600}{20} }{\frac{19r}{20} } }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{3r+1600}{\cancel{20}} \times \dfrac{\cancel{20}}{19r} }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{3r+1600}{19r} }\\\\\\\mapsto\sf{19r=15r+8000}$

$\mapsto\sf{19r-15r=8000}\\\\\\\mapsto\sf{4r=8000}\\\\\\\mapsto\sf{r=\cancel{\dfrac{8000}{4} }}\\\\\\\mapsto\sf{\red{r=Rs.2000}}$

Thus,

$\underbrace{\sf{The\:cost\:price\:(C.P.)\:of\:table\:=\:r\:=Rs.2000.}}}}}$

Answer 2

Answer:

AnswEr :

Rs.2000.

\bf{\orange{\underline{\underline{\bf{Given\::}}}}}

Given:

A person sells a table at a profit of 10%. If he have brought the table at 5% less cost sold for 80 more. He would have gained 20%.

The cost price of table.

\bf{\green{\underline{\underline{\bf{Explanation\::}}}}}

Explanation:

Let the Cost price (C.P.) be Rs.r

Formula use :

\star⋆ A person sells a table at a profit of 10% :

\begin{lgathered}\mapsto\sf{S.P.=\dfrac{100+10}{100} \times r}\\\\\\\mapsto\sf{S.P.=\dfrac{11\cancel{0}}{10\cancel{0}} \times r}\\\\\\\mapsto\sf{\red{S.P.=\dfrac{11r}{10} }}\end{lgathered}

↦S.P.=

100

100+10

×r

↦S.P.=

10

0

11

0

×r

↦S.P.=

10

11r

\star⋆ Cost price of the table 10 % loss :

\begin{lgathered}\mapsto\sf{S.P.=\dfrac{100-5}{100} \times r}\\\\\\\mapsto\sf{S.P.=\cancel{\dfrac{95}{100}} \times r}\\\\\\\mapsto\sf{\red{S.P.=\dfrac{19r}{20} }}\end{lgathered}

↦S.P.=

100

100−5

×r

↦S.P.=

100

95

×r

↦S.P.=

20

19r

Now;

\begin{lgathered}\mapsto\sf{20\%=\dfrac{S.P.-C.P.}{C.P.} }\\\\\\\mapsto\sf{\dfrac{20}{100} =\dfrac{\frac{11r}{10}+80-\frac{19r}{20} }{\frac{19r}{20} } }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{\frac{22r+1600-19r}{20} }{\frac{19r}{20} } }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{\frac{3r+1600}{20} }{\frac{19r}{20} } }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{3r+1600}{\cancel{20}} \times \dfrac{\cancel{20}}{19r} }\\\\\\\mapsto\sf{\dfrac{1}{5} =\dfrac{3r+1600}{19r} }\\\\\\\mapsto\sf{19r=15r+8000}\\\\\\\end{lgathered}

↦20%=

C.P.

S.P.−C.P.

↦

100

20

=

20

19r

10

11r

+80−

20

19r

↦

5

1

=

20

19r

20

22r+1600−19r

↦

5

1

=

20

19r

20

3r+1600

↦

5

1

=

20

3r+1600

×

19r

20

↦

5

1

=

19r

3r+1600

↦19r=15r+8000

\begin{lgathered}\mapsto\sf{19r-15r=8000}\\\\\\\mapsto\sf{4r=8000}\\\\\\\mapsto\sf{r=\cancel{\dfrac{8000}{4} }}\\\\\\\mapsto\sf{\red{r=Rs.2000}}\end{lgathered}

↦19r−15r=8000

↦4r=8000

↦r=

4

8000

↦r=Rs.2000

Thus,