Ramesh bought two boxes for Rs 1300. He sold one box at a profit of \[20\% \] and the other box at a loss of \[12\% \] . If the selling price of both boxes is the same, find the cost price of each box.

Hint: Here in this question, we will find the cost of each box. To solve this, we have to find the selling price of each box. Selling price of first box can be find by using a profit percentage and selling price of second box can be find by using a loss percentage later by given statement i.e., selling price of both boxes is same means equate selling price of two boxes and by further simplification, we get the required solution.

Complete step-by-step answer:
Given,
Ramesh bought two boxes for Rs 1300.
Let us take the cost price of \[{1^{st}}\] box = \[x\] Rs
Then, the cost price of \[{2^{nd}}\] box is = \[1300 - x\] Rs.
Ramesh sold one box at a profit of \[20\% \]
Now, the selling price of \[{1^{st}}\] box is:
 \[ \Rightarrow cost\;price + \dfrac{{profit\% }}{{100}} \times cost\;price\]
 \[ \Rightarrow x + \dfrac{{20}}{{100}} \times x\]
 \[ \Rightarrow \dfrac{{100x + 20x}}{{100}}\]
 \[ \Rightarrow \dfrac{{120x}}{{100}}\] -----------(1)
Ramesh sold other box at a loss of \[12\% \] , then
The selling price of \[{2^{nd}}\] box is:
 \[ \Rightarrow cost\;price - \dfrac{{loss\% }}{{100}} \times cost\;price\]
 \[ \Rightarrow \left( {1300 - x} \right) - \dfrac{{12}}{{100}} \times \left( {1300 - x} \right)\]
 \[ \Rightarrow \dfrac{{100\left( {1300 - x} \right) - 12\left( {1300 - x} \right)}}{{100}}\]
 \[ \Rightarrow \dfrac{{114400 - 88x}}{{100}}\] ----------(2)
Given, the selling price of both boxes is the same, then
 \[ \Rightarrow Selling{\text{ }}\;price{\text{ }}\;of\;{1^{st}}box{\text{ }} = {\text{ }}selling{\text{ }}\;price\;of\;{2^{nd}}\;box\]
From equation (1) and (2), then
 \[ \Rightarrow \dfrac{{120x}}{{100}} = \dfrac{{114400 - 88x}}{{100}}\]
Multiply both side by 100, then we have
 \[ \Rightarrow 120x = 114400 - 88x\]
Add both side by \[88x\] , then
 \[ \Rightarrow 120x + 88x = 114400 - 88x + 88x\]
 \[ \Rightarrow 208x = 114400\]
Divide both side by 208, we get
 \[ \Rightarrow x = \dfrac{{114400}}{{208}}\]
On simplification, we get
 \[ \Rightarrow x = 550\]
Hence,
The cost price of \[{1^{st}}\] box \[x = 550\] Rs
The cost of \[{2^{nd}}\] box = \[1300 - x\]
 \[ \Rightarrow 1300 - 550\]
 \[ \Rightarrow 750\] Rs
Therefore, the cost price of two boxes are 500 Rs and 750 Rs Respectively.

Note: These types of questions are general aptitude questions, to solve this remember the concept of profit and loss. Profit means the amount gained by selling a product with more than its cost price at profit the selling price is the sum of cost price and the profit price and loss means the amount the seller incurs after selling the product less than its cost price at loss the selling price is the difference between the cost price and the lost price.