Question

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

Answer 1

Hint: The given problem is based on profit and loss concept; in this problem we can find profit percentage using the formula $$\left({\displaystyle \frac{profit}{cp}}\right)\times 100$$and to find the selling price of first two tables we can make use of the formula $$sp=\left({\displaystyle \frac{100+profit\mathrm{\%}}{100}}\right)\times cp$$ and $$sp=\left({\displaystyle \frac{100-loss\mathrm{\%}}{100}}\right)\times cp$$ 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 $$sp=\left({\displaystyle \frac{100+profit\mathrm{\%}}{100}}\right)\times cp$$
$$\Rightarrow$$ given The Selling price of the first table at $$8\mathrm{\%}$$ profit by using above formula
we get =$$\left({\displaystyle \frac{100+8}{100}}\right)\times 2500$$
$$\therefore$$ The Selling price of the first table=2700 Rs
Now we have to calculate selling price of the first table using the formula $$sp=\left({\displaystyle \frac{100-loss\mathrm{\%}}{100}}\right)\times cp$$
$$\Rightarrow$$ given The Selling price of the second table at $$3\mathrm{\%}$$ loss by using above formula
we get =$$\left({\displaystyle \frac{100-3}{100}}\right)\times 2500$$
$$\therefore$$ 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
$={\displaystyle \frac{100}{2500}}\times 100\mathrm{\%}$
$$\begin{gathered} ={\displaystyle \frac{100}{2500}}\times 100\mathrm{\%} \\ =4\mathrm{\%} \end{gathered}$$
$=4\mathrm{\%}$
 Therefore, profit percent on third table is $$4\mathrm{\%}$$
So, the correct answer is “ $$4\mathrm{\%}$$”.

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.