Question

Arun purchased \[\;30kg\] of wheat at the rate of \[11.50Rs.\;per{\text{ }}kg\] and $20kg$ of wheat at the rate of \[\;14.25per{\text{ }}kg\]. He mixed the two and sold the mixture. Approximately what price per kg should be sold to make $30\% $ profit ?
A) \[17.80Rs.\]
B) $14.38Rs.$
C) $14Rs.$
D) $15.40Rs.$

Answer 1

Hint: In order to calculate the sale price first we need to find the total cost price relative to the total money spent by Arun further we will find the benefit and finally by adding cost price and income we will get our response.

Complete step-by-step answer:
Given that arun purchased \[\;30kg\] of wheat at the rate of \[11.50Rs.\;per{\text{ }}kg\] and $20kg$ of wheat at the rate of \[\;14.25per{\text{ }}kg\].

Now we are going to calculate overall cost price

According to the statement, then

\[30kg\] at \[11.50Rs.\;per{\text{ }}kg\] \[ = {\text{ }}30{\text{ }} \times {\text{ }}11.50{\text{ }} = {\text{ }}345Rs.\]

$20kg$ at \[\;14.25per{\text{ }}kg\] \[ = {\text{ }}20{\text{ }} \times 14.25{\text{ }} = {\text{ }}285Rs.\]

Total cost \[ = {\text{ }}345{\text{ }} + {\text{ }}285{\text{ }} = {\text{ }}630Rs.\]


Now, we will find the profit that will be $30\% $ of total cost price so we have

Profit = $30\% $ of \[630Rs.\]

Profit \[ = {\text{ }}0.3{\text{ }} \times {\text{ }}630{\text{ }} = {\text{ }}189Rs.\]

As we know that selling price is equal to the addition of total cost price and profit

So, Selling Price = Cost Price + Profit

Selling Price \[ = {\text{ }}630{\text{ }} + {\text{ }}189{\text{ }} = {\text{ }}819Rs\]

We must divide the obtained sales price by total material weight \[\left( {30{\text{ }}kg{\text{ }} + 20{\text{ }}kg{\text{ }} = {\text{ }}50{\text{ }}kg} \right)\] to determine for per kg

Selling Price per kg \[ = {\text{ }}819{\text{ }} \div {\text{ }}\left( {30{\text{ }} + {\text{ }}20} \right){\text{ }} = {\text{ }}16.38Rs.\]

Hence the correct answer is option B.

Note- When the selling price is greater than the cost price then we can define profit as \[SP - CP\] and if the cost price is greater than the selling price then loss will occur that is given by \[CP - SP\]. Profit percentage and loss percentage are always measured on cost price.