Question

The cost price of item B is Rs. 200- more than the cost price of item A. Item A was sold at a profit of 20% and item B was sold at a loss of 30%. If the respective ratio of selling price of item $A$and $B$ is 6:7, what is the cost price of item $B$.

Answer 1

Hint: Here we will proceed by using the approach of cost price and selling price. Then by applying the conditions given in the question we will get our answer.
Let the cost price of item $A$ (C.P.) will be Rs. $x$.

Complete step-by-step solution -
Then the cost price (C.P.) of item $B$ Rs. $\left( {x + 200} \right)$
On selling,
Profit on item $A$ $ = 20\% $
That is, $20\% $of $x$
$ = \dfrac{{20x}}{{100}}$
$ = \dfrac{{2x}}{{10}}$
Thus, selling prices (S.P.) of item $A$ will be equal to the sum of its Cost prices (C.P.) and the profit on its S.P. $ = C.P. + Profit$
$ \Rightarrow $S.P. $ = x + \dfrac{{2x}}{{10}}$
    $ = \dfrac{{10x + 2x}}{{10}}$
    $ \Rightarrow $S.P. $ = \dfrac{{12x}}{{10}}$
  Now, Loss on item $B = $30%
 That is 30% of $\left( {x + 200} \right)$
 =$\dfrac{{30}}{{100}}\left( {x + 200} \right)$
$ = \dfrac{{3x}}{{10}} + 60$ Thus the selling price (S.P.) of item $B$ will be equation to
 $S.P. = C.P. - Loss$
 $ \Rightarrow S.P. = \left( {x + 200} \right) - \left( {\dfrac{{3x}}{{10}} + 60} \right)$
 $
   \Rightarrow S.P. = \dfrac{{7x + 1400}}{{10}} \\
   \Rightarrow S.P. = \dfrac{{7x + 1400}}{{10}} \\
 $
But, it is also given in the question that the respective ratios of selling prices of item $A$ and $B$ is $6:7$
Therefore, $\dfrac{{S.P. \text{of}\ \text{item}\ \text{A}}}{{S.P. \text{of}\ \text{item}\ \text{B}}} = \dfrac{6}{7}$
     $ \Rightarrow \dfrac{{\dfrac{{12x}}{{10}}}}{{\dfrac{{7x + 1400}}{{10}}}} = \dfrac{6}{7}$
       $ \Rightarrow \dfrac{{12x}}{{7x + 1400}} = \dfrac{6}{7}$
       $ \Rightarrow \dfrac{{7x + 1400}}{{12x}} = \dfrac{7}{6}$ …. (By taking reciprocal)
        $ \Rightarrow \dfrac{{7\left( {x + 200} \right)}}{{12x}} = \dfrac{7}{6}$
        $ \Rightarrow \dfrac{{x + 200}}{x} = \dfrac{7}{6} \times \dfrac{{12}}{7}$
    By simplifying, we will get,
  $ \Rightarrow \dfrac{{x + 200}}{x} = 2$
$ \Rightarrow x = 200$
 Therefore, Cost Prices of item $A$ will be Rs. 200
And, Cost price of item $A$ will be
 Rs. $x + 200 = 200 + 200$ (Putting the value of x that is 200)
$ = Rs.400$

Note: Whenever we come up with this type of problem, we must find out the value of S.P. or C.P. first with respect to profit then with respect to loss. After that we have to calculate their ratios. By using these basics we can easily solve this question.