Question

A cloth seller marks a dress at 45% above the cost price and allows a discount of 20
%. What profits does he make in selling the dress?

Answer 1

Hint: Since the cost price is not given so we have to consider the cost price as 100. It is given
that the seller increases 45% on the cost price. So from that we need to find the selling price of
that cloth. Since the discount is 20%, we have to reduce 20% from that selling price to get the
price at which the seller actually sells the cloth. For profit, finally we have to subtract the cost
price 100 from the price at which the seller actually sale the cloth. When we divide the profit
with the cost price then converting into the percentage we get our profit gain on that cloth.
Let the cost price is 100
It is given that the seller increases 45% on the cost price
Find the selling price of the dress.
$\begin{array}{c}{\rm{Selling price}} = 100 + 45\% 100\\ = 100 + \dfrac{{45 \times
100}}{{100}}\\ = 100 + 45\\ = 145\end{array}$
Since the seller give discount of 20%.
Find the price after discount.
$\begin{array}{c}{\rm{Price}} = 145 - 20\% \;{\rm{of}}\;145\\ = 145 - 145 \times
\dfrac{{20}}{{100}}\\ = 145 - 29\\ = 116\end{array}$

Now, we have to calculate the amount of profit.
Profit$\begin{array}{c} = 116 - 100\\ = 16\end{array}$

Now, calculating the percentage gain of the profit.

Percentage gain$\begin{array}{c} = \dfrac{{16}}{{100}} \times 100\\ = 16\% \end{array}$

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 gets profit
and if the selling price is less than the cost price then it is said to be the loss of the seller in that item.
Here we have to determine the percentage gain on that cloth. Since the increase in percentage of
the selling price and the discount is given we can calculate the selling price by considering the
cost price. With these data we can calculate the amount of profit and the percentage gain on that
cloth.