Question

Sarita bought eggs at Rs.\[8.40\] a dozen. At what price per hundred must she sell them so as to earn a profit of \[15 \%\]?

Answer 1

Hint: Here, we will first find the cost price of one egg using the unitary method and then multiply it by 100 to get the cost price of 100 eggs. Then we will substitute all the values in the profit percentage formula and solve the equation to get the value of the selling price of 100 eggs.

Formula used:
 \[{\rm{Profit}}\% = \dfrac{{SP - CP}}{{CP}} \times 100\], \[CP\] is the cost price of the object and \[SP\] is the selling price of the object.

Complete step-by-step answer:
It is given to us that Sarita bought a dozen eggs for Rs. \[8.40\]. So,
Cost Price of 12 eggs \[ = Rs8.4\]
By using the unitary method, we get
Cost Price of 1 egg \[ = \dfrac{{8.4}}{{12}} = 0.7\]
So, Cost Price of 1 egg is Rs. \[0.7\].
Now, we will find the cost price of 100 eggs by multiply 100 by the cost price of 1 egg. Therefore, we get
Cost Price of 100 eggs \[ = 0.7 \times 100 = 70\]
So, Cost Price of 100 eggs is Rs.70.
Let Selling Price per 100 eggs be \[y\].
It is given to us that she should earn a profit of \[15\% \].
Substituting \[CP = 70\], \[{\rm{Profit}}\% = 15\% \] and \[SP = y\] equation \[{\rm{Profit}}\% = \dfrac{{SP - CP}}{{CP}} \times 100\] we get,
\[15 = \dfrac{{y - 70}}{{70}} \times 100\]\[\]
On cross multiplication, we get
\[ \Rightarrow y - 70 = \dfrac{{15 \times 70}}{{100}}\]
Adding 70 on both the sides, we get
\[ \Rightarrow y = \dfrac{{15 \times 70}}{{100}} + 70\]
Simplifying the equation, we get
\[ \Rightarrow y = 10.5 + 70\]
Adding the terms, we get
\[ \Rightarrow y = 80.5\]
Therefore, to gain a profit of \[15\% \] Sarita should sell the eggs for Rs.\[80.5\] per hundred.

Note: Cost price is the price at which a product is purchased. The price at which the product is sold by the seller is called the selling price. When the selling price is greater than the cost price then there will be profit. But when the selling price is less than the cost price then there will be a loss. There is a difference between the profit value and profit percentage which is to be considered while solving a problem.