Question

The difference between selling an article at \[6\%\] profit and at \[9\%\] profit is \[Rs.9\]. Find the sum of two selling prices.

Answer 1

Hint: In order to find the sum of two selling prices, firstly we will be finding the net profit percent and then we will be finding the cost price with the help of profit and selling price given. Then we will be finding the selling prices at both profit percents and upon adding up the prices we obtain the required answer.

Complete step-by-step solution:
Now let us learn about selling price and cost price. The price at which a good is being bought is considered as cost price. In the same way, the price at which the goods are being sold is called the selling price. While comparing the cost price and selling price, if the cost price is greater than the selling price, then loss occurs. If the selling price is greater than the cost price, then gain or profit occurs.
Now let us start solving our problem.
We are given that difference between selling at different profits as \[Rs.9\].
We get difference between the profit percents as \[9\%-6\%=3\%\]
So we can say that \[3\%\] of CP would be \[9\].
Now let us find the cost price of the article. We get,
\[\Rightarrow \dfrac{9\times 100}{3}=Rs.300\]
The cost price is \[Rs.300\].
Now let us find the selling price of the article at different gain percents, we get
The formula for this would be
 \[\Rightarrow \dfrac{100+gain}{100}\times CP\]
We have two gain cases,
The SP when the gain is \[6\%\] is
\[\Rightarrow \dfrac{100+6}{100}\times 300=106\times 3=Rs.318\]
The SP when the gain is \[9\%\] is
\[\Rightarrow \dfrac{100+9}{100}\times 300=109\times 3=Rs.327\]
\[\therefore \] The sum of two selling prices is \[Rs.318+Rs.327=Rs.645\]

Note: We must have a note that when one or more gain percentages are given, we must be considering the net profit percent for the calculation of cost price. We can apply the concept of gain and loss percentages in everyday life to calculate the corresponding loss and gain values.