Question

Reena bought two tables for Rs. 1800 each. She sold one at a loss of 8% and the other at a profit of 12%. Find the selling price of each. Also, find out the total profit or loss.

Answer 1

Hint: The cost price of the first table and the second table is Rs. 1800. The cost price of both tables is Rs. 3600. Reena sold the first table at a loss of 8%. It means that the selling price of the first table is 8% less than the original cost price of the table. So, the selling price of the first table is Rs. \[\left( 1800\text{ }\text{ }-8\%\text{ }of\text{ }1800 \right)\] . Reena sold the second table at a profit of 12%. It means that the selling price of the second table is 12% more than the original cost price of the table. So, the selling price of the second table is Rs. \[\left( 1800\text{ + 12}\%\text{ }of\text{ }1800 \right)\] . The selling price of both tables is Rs. \[\left( 1800\text{ }\text{ }-8\%\text{ }of\text{ }1800 \right)+\left( 1800\text{ + 12}\%\text{ }of\text{ }1800 \right)\] . We know that Profit is the difference between the selling price and the cost price,
\[\text{Profit=Selling}\,\text{price-Cost}\,\text{price}\] . Now, use this formula and calculate the total profit.

Complete step by step solution:
According to the question, it is given that Reena bought two tables for Rs. 1800 each. She sold one at a loss of 8% and the other at a profit of 12%.
Here, we have two cases, \[{{1}^{st}}\] case and \[{{2}^{nd}}\] case.
In \[{{1}^{st}}\] case, we have
The cost price of the first table = Rs. 1800 ……………………….(1)
The cost price of the second table = Rs. 1800 ……………………….(2)
The cost price of both tables = Rs. \[\left( 1800+1800 \right)\] = Rs. 3600 …………………………(3)
In \[{{2}^{nd}}\] case, it is given that
Reena sold the first table at a loss of 8%. It means that the selling price of the first table is 8% less than the original cost price of the table.
From equation (1), we have the cost price of the first table. So,
The selling price of the first table = Rs. \[\left( 1800\text{ }\text{ }-8\%\text{ }of\text{ }1800 \right)\] = Rs. \[1800-\dfrac{8}{100}\times 1800\] = Rs.
\[1800-8\times 18\] = Rs. \[\left( 1800-144 \right)\] = Rs. 1656 ……………………………(4)
Reena sold the second table at a profit of 12%. It means that the selling price of the second table is 12% more than the original cost price of the table.
From equation (2), we have the cost price of the second table. So,
The selling price of the second table = Rs. \[\left( 1800\text{ + 12}\%\text{ }of\text{ }1800 \right)\] = Rs. \[1800+\dfrac{12}{100}\times 1800\] = Rs. \[1800+12\times 18\] = Rs. (1800 + 216) = Rs. 2016 ……………………………(5)
From equation (4) and equation (5), we have the selling price of the first table and second table.
Therefore, the selling price of both tables = Rs. \[\left( 2016+1656 \right)\] = Rs. 3672 ………………………(6)
We know that Profit is the difference between the selling price and the cost price,
\[\text{Profit=Selling}\,\text{price-Cost}\,\text{price}\] ……………………………(7)
From equation (3), we have the cost price of both tables and from equation (6), we have the selling price of both tables.
Now, from equation (3), equation (6), and equation (7), we get
\[\text{Profit=Rs}\text{.}\left( 3672-3600 \right)=\text{Rs}\text{.72}\] ………………………….(8)
So, the value of the profit is Rs. 72.
From equation (4) and equation (5), we have the selling price of the first table and second table. Also, from equation (8) we have got the value of the profit.
Therefore, the selling price of the first table and second table is Rs. 1656 and Rs. 2016 respectively, and the total profit is Rs. 72.

Note: In this question, one might think that the cost price of both tables is Rs. 1800 and take the cost price of the first table and second table equal to Rs. 900. This is wrong because it is given that the cost price of each table is Rs. 1800. Therefore, the cost price of the first table and second table equal to Rs. 1800.