Question

45 packets of butter each weighing $100$ grams costs rupees $607.50$ . What will the cost of $18$ packets of butter each weighing $500$ grams ?
$\left( {\text{A}} \right){\text{ }}1215Rs.$
$\left( {\text{B}} \right){\text{ }}1325Rs.$
$\left( {\text{C}} \right){\text{ }}1430Rs.$
$\left( {\text{D}} \right){\text{ }}1475Rs.$

Answer 1

Hint: This is a very basic question based on the concept of comparing quantities. There is some basic terminology related to this concept. $\left( 1 \right)$ Cost price (CP) : The actual price at which the product is bought or the buying price of an item. $\left( 2 \right)$ Selling price (SP) : It is the price at which the product is sold out by the retailer. In this question, the cost price of a certain item for a specific quantity has been given and on the basis of that we are asked to calculate the cost price for another quantity . The easiest way to solve this question is to calculate the cost price for the $1$ unit of the item and then cost of the asked quantity can be found out by multiplying it with the cost of $1$ item.

Complete step-by-step solution:
Although the easier approach is mentioned above, this question can also be solved like this;
Given : $45$ packets of butter of $100$ grams each means $45 \times 100 = 4500grams$ ;
Hence, we can say that the cost of $4500grams$ is $607.50Rs.$
According to the question, we have to calculate the cost of $18$ packets of butter each weighing $500grams$ ;
Therefore, $18Packets \times 500grams = 9000grams$ ;
Since the cost of $4500grams = 607.50Rs.$ ;
Therefore, the cost of $9000grams$ i.e. $4500grams \times 2$ will be ;
$=607.50 \times 2 = 1215Rs.$
Therefore, the correct answer for this question is option $\left( {\text{A}} \right){\text{ i}}{\text{.e}}{\text{. }}1215Rs.$
                                                             OR
We can calculate the cost of $1{\text{ gram}}$ of butter as ;
$\because 4500grams = 607.50Rs.$
$\therefore 1gram = \dfrac{{607.50}}{{4500}} = 0.135Rs.$
Now, we can calculate the value for $9000grams$ as ;
$ =9000 \times 0.135 = 1215Rs.$

Note: This question has been solved above using two methods. The first method is a non-conventional but easier approach in this case. By simple observation we can solve the question using the first approach. The Second method is a standard or conventional method means it can be applied always. Some additional terms related to the concept of buying and selling are : $\left( 1 \right)$ Profit: After selling a product, if the seller makes some extra money over the cost money, then it is called profit. It is mathematically stated as: ${\text{Profit = Selling price }} - {\text{ Cost price}}$ . The profit percentage can be calculated as : ${\text{Profit}}\% = \dfrac{{{\text{Profit}}}}{{{\text{Cost price}}}} \times 100$ . $\left( 2 \right)$ Loss : If the seller has to sell the product at a price even less than its cost price , then it is termed as a loss. It is mathematically stated as: ${\text{Loss = Cost price }} - {\text{ Selling price}}$ . The loss percentage can be calculated as : ${\text{Loss }}\% {\text{ = }}\dfrac{{{\text{Loss}}}}{{{\text{Cost price}}}} \times 100$.