Question

A trader sold an article at a loss of $5\% $ but when he increased the selling price by $Rs.65$ he gained $3.33\% $ on the cost price. If he sells the same article at $Rs.936$, what is the profit percentage?

Answer 1

Hint:Here, in the given question, we are given that a trader sold an article at a loss of $5\% $ but when he increased the selling price by $Rs.65$ he gained $3.33\% $ on the cost price, we need to find the profit percentage when he sells the same article at $Rs.936$. We are given a change in percentage and a change in price. To find the profit percent when an article is sold at $Rs.936$, we first need to find the percentage for $Rs.1$. Using this, we will find the profit percentage for $Rs.936$.

Complete step by step answer:
To find: profit percentage if he sells article at $Rs.936$
Change in percentage = $3.33 + 5 = 8.33\% $
Change in price = $Rs.65$
The percentage if he sells for $Rs.65$ is $8.33\% $
The percentage if he sells for $Rs.1$ will be, $\dfrac{{8.33}}{{65}}$
To remove the decimal we will multiply the denominator with $100$.
$\dfrac{{833}}{{65 \times 100}}$
On multiplication, we get
$\dfrac{{833}}{{6500}}$
Similarly, the percentage if he for $Rs.936$ will be,
$\dfrac{{833}}{{6500}} \times 936= 120\% $
Thus, profit = $120\% - 100\% = 20\% $

Therefore, if the trader sells the article at $Rs.936$, the profit percent will be $20\% $.

Note:We can solve this type of questions using formulas also. Remember that profit or loss percentage is always calculated on cost price of an item, until and unless it is mentioned to calculate the percentage on selling price.
For profit percentage: $Profit\% = \dfrac{{S.P - C.P}}{{C.P}} \times 100$
For loss percentage: $Loss\% = \dfrac{{C.P - S.P}}{{C.P}} \times 100$