Question

A dealer sells a table at 20% profit. Had he purchased it for 6% lesser cost and sold for
Rs.50 less he would have earned a profit of 25%. Find the cost of the table.

Answer 1

Hint: Since the cost price is not given so we have to consider the cost price (suppose $x$). It is
given that the dealer increases 20% on the cost price. So from that we need to find the selling
price of that table. In the question it is given that dealer purchased the table at 6% lesser cost and
sold for Rs.50 less. From that we have to find the new cost price and the new selling price of the
table. By subtracting the new cost price from the selling price we have to find the amount of
profit earned on that table. It is given that the dealer earned a profit of 25%. So we have to equate
both the profit and solve for $x$.

Let the cost of the table is $x$.
Given that the dealer earned 20% profit on the cost price.
Therefore the selling price of the dealer $\begin{array}{c} = x + x \times \dfrac{{20}}{{100}}\\
= \dfrac{{120}}{{100}}x\\ = \dfrac{6}{5}x\end{array}$

It is given that the dealer purchased it for 6% less cost.
Now, find the new cost price.
$\begin{array}{c}{\rm{New}}\;{\rm{cost}}\;{\rm{price}} = x - \dfrac{6}{{100}} \times x\\ =
\dfrac{{94}}{{100}}x\\ = \dfrac{{47}}{{50}}x\end{array}$ (1)
Dealer sells that table with the loss of Rs.50 from the original selling price $\dfrac{6}{5}x$.
Therefore the new selling price $ = \dfrac{6}{5}x - 50$
(2)
Now, we have to calculate the profit earned by selling that table.
New profit = New selling price – New cost price
$\begin{array}{l} = \dfrac{6}{5}x - 50 - \dfrac{{47}}{{100}}x\\ =
\dfrac{{26}}{{100}}x - 50\end{array}$
(3)
It is given that the dealer earned a profit of 25%.
Therefore profit$ = 25\% \;{\rm{of}}\;\dfrac{{47}}{{50}}x$
$\begin{array}{l} = \dfrac{{25}}{{100}} \times \dfrac{{47}}{{50}}x\\ =
\dfrac{{47}}{{200}}x\end{array}$ (4)
Now, comparing (3) and (4) and solving for $x$.

$\begin{array}{l}\dfrac{{26}}{{100}}x - 50 = \dfrac{{47}}{{200}}x\\ \Rightarrow
\dfrac{{26}}{{100}}x - \dfrac{{47}}{{200}}x = 50\\ \Rightarrow \dfrac{{52x - 47x}}{{200}}
= 50\\ \Rightarrow \dfrac{{5x}}{{200}} = 50\\ \Rightarrow x = 2000\end{array}$
Hence, the required cost price of the table is Rs.2000.

Note: Cost price is the original price at which the seller bought the item. Selling price is the price
at which seller sells the item. If selling price is more than the cost price than the seller got profit
and if the selling price is less than cost price then it is said to be the loss of the seller in that item.
Here we have to determine the cost price of the table. Since the increasing percentage of the
selling price is given, we can calculate the selling price by considering the cost price. The
Percentage gain on that table is given. Thus, comparing the given profit with the calculated
profit, we can determine the cost price of the table.