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# Three tables are purchased for Rs.$2500$ each. First is sold at a profit of $8\%$, the second is sold at a loss of $3\%$. If their average selling price is Rs.$2575$, find the profit percent on the third.

Last updated date: 01st Mar 2024
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Hint: The given problem is based on profit and loss concept; in this problem we can find profit percentage using the formula $\left( {\dfrac{{profit}}{{cp}}} \right) \times 100$and to find the selling price of first two tables we can make use of the formula $sp = \left( {\dfrac{{100 + profit\% }}{{100}}} \right) \times cp$ and $sp = \left( {\dfrac{{100 - loss\% }}{{100}}} \right) \times cp$ as per the requirement of the problem.

Complete step by step solution:
Given The cost of $1$ table = Rs.$2500$.
Then, the Cost price of the three tables = Rs. $2500 \times 3 = 7500$
Given The average Selling price of the $3$ tables = Rs. $2575$.
Then, the total Selling price = Rs. $2575 \times 3 = 7725$
Now we have to calculate selling price of the first table using the formula $sp = \left( {\dfrac{{100 + profit\% }}{{100}}} \right) \times cp$
$\Rightarrow$ given The Selling price of the first table at $8\%$ profit by using above formula
we get =$\left( {\dfrac{{100 + 8}}{{100}}} \right) \times 2500$
$\therefore$ The Selling price of the first table=2700 Rs
Now we have to calculate selling price of the first table using the formula $sp = \left( {\dfrac{{100 - loss\% }}{{100}}} \right) \times cp$
$\Rightarrow$ given The Selling price of the second table at $3\%$ loss by using above formula
we get =$\left( {\dfrac{{100 - 3}}{{100}}} \right) \times 2500$
$\therefore$ The Selling price of the second table=2425 Rs
Then, the sum of the Selling price of two tables = $(2700 + 2425) = 5125$
So, the Selling price of the third table = The total of the Selling price − the sum of the Selling price of two tables
$= (7725 - 5125) = 2600$Rs
Profit on the third tables $= (2600 - 2500) = 100$Rs
$= \dfrac{{100}}{{2500}} \times 100\%$
$= \dfrac{{100}}{{2500}} \times 100\% \\ = 4\% \\$
$= 4\%$
Therefore, profit percent on third table is $4\%$
So, the correct answer is “ $4\%$”.

Note: To solve the above problem we have used the direct formula along with unitary method (if the value of one unit is given then multiply the value of a single unit to the number of units to get necessary value) where ever necessary because as in the problem cost of each table is given.