Question

An article is sold at 25% profit if the CP and SP of the article increased by Rs.60 and Rs.30 respectively the profit percentage decreases by 15% find the cost price of the article

Answer 1

We know that profit percentage,

$\longrightarrow\sf{P=\dfrac{SP-CP}{CP}\times100}$

Since the article is sold at 25% profit first,

$\longrightarrow\sf{P=25}$

$\longrightarrow\sf{\dfrac{SP-CP}{CP}\times100=25}$

$\longrightarrow\sf{\dfrac{SP-CP}{CP}=\dfrac{25}{100}}$

$\longrightarrow\sf{\dfrac{SP-CP}{CP}=\dfrac{1}{4}}$

$\longrightarrow\sf{SP-CP=\dfrac{CP}{4}\quad\quad\dots(1)}$

Now CP and SP are increased by Rs.60 and Rs.30 respectively.

Then the profit percentage decreases by 15%, i.e., it becomes 10%.

[Note:- Old profit percentage 25% was of old CP. New profit percentage 10% is of new CP.]

$\longrightarrow\sf{P'=10}$

$\longrightarrow\sf{\dfrac{(SP+30)-(CP+60)}{CP+60}\times100=10}$

$\longrightarrow\sf{\dfrac{SP+30-CP-60}{CP+60}=\dfrac{10}{100}}$

$\longrightarrow\sf{\dfrac{SP-CP-30}{CP+60}=\dfrac{1}{10}}$

From (1),

$\longrightarrow\sf{\dfrac{CP}{4}-30=\dfrac{CP+60}{10}}$

$\longrightarrow\sf{\dfrac{CP}{4}-30=\dfrac{CP}{10}+6}$

$\longrightarrow\sf{\dfrac{CP}{4}-\dfrac{CP}{10}=30+6}$

$\longrightarrow\sf{\dfrac{6\,CP}{40}=36}$

$\longrightarrow\sf{\underline{\underline{CP=240}}}$

Hence the cost price of the article is $\bf{Rs.240.}$