Question

John bought 100 eggs for Rs 40. Out of these, four eggs were found to be broken and he sold the remaining eggs at the rate of Rs 7.50 per dozen. Find his gain or loss per cent.

Answer 1

Hint:
Here, we will find the gain or loss per cent. First, we will find the cost price of 1 egg and then the cost price of 96 eggs. We will find the selling price of 96 eggs. We will be using the profit/ loss formula to find the profit/ loss and by using the profit/ loss percentage we will find the gain or loss percent.

Formula Used:
We will use the following formulas:
1. Profit is given by the formula \[{\rm{Profit}} = S.P. - C.P.\]
2. Profit Percentage is given by the formula \[{\rm{Profit\% }} = \dfrac{{{\rm{Profit}}}}{{C.P.}} \times 100\]

Complete Step by step Solution:
We are given that John bought 100 Eggs for Rs 40.
Cost Price of 100 Eggs \[ = {\rm{Rs}}.40\]
Now, we will find the Cost Price of 1 Egg by dividing the total Cost Price of 100 Eggs by the total Number of eggs.
\[ \Rightarrow \] Cost Price of 1 Egg \[ = \dfrac{{40}}{{100}}\]
Dividing the terms, we get
\[ \Rightarrow \] Cost Price of 1 Egg \[ = {\rm{Rs}}.0.40\]
We are also given that out of these, four eggs were found to be broken and he sold the remaining eggs at the rate of \[{\rm{Rs}}7.50\] per dozen.
We know that 1 dozen is equal to a pack of 12 eggs.
Number of good eggs \[ = \] Total number of eggs \[ - \] Number of broken eggs
Substituting the values in the above equation, we get
\[ \Rightarrow \] Number of good eggs \[ = 100 - 4\]
Subtracting the terms, we get
\[ \Rightarrow \] Number of good eggs \[ = 96\]
We know that ,
 Selling Price of a dozen of eggs \[ = {\rm{Rs}}.7.50\]
Now, we will find the Selling Price of 8 dozen Eggs by multiplying the Selling Price of a dozen of Eggs by the Number of dozen eggs.
\[ \Rightarrow \] Selling Price of 8 dozen of eggs \[ = {\rm{Rs}}.7.50 \times 8\]
Multiplying the terms, we get
\[ \Rightarrow \] Selling Price of 8 dozen of eggs \[ = {\rm{Rs}}.60\]
Now, we will find the Cost Price of 96 eggs by multiplying the Cost Price of an Egg by the Number of eggs.
 Cost Price of 96 eggs \[ = {\rm{Rs}}0.4 \times 96\]
\[ \Rightarrow \] Cost Price of 96 eggs \[ = {\rm{Rs}}38.4\]
Since the Selling Price of 96 Eggs is greater than the Cost Price of 96 Eggs i.e.,\[S.P. > C.P.\] so there is a Profit.
Profit is given by the formula \[{\rm{Profit}} = S.P. - C.P.\]
Substituting the values in the above formula, we get
\[ \Rightarrow {\rm{Profit}} = Rs.60 - Rs.38.4\]
\[ \Rightarrow {\rm{Profit}} = Rs.21.6\]
Profit Percentage is given by the formula \[{\rm{Profit\% }} = \dfrac{{{\rm{Profit}}}}{{C.P.}} \times 100\]. Therefore, we get
\[{\rm{Profit\% }} = \dfrac{{21.6}}{{38.4}} \times 100\]
\[ \Rightarrow {\rm{Profit\% }} = 0.5625 \times 100\]
Multiplying the terms, we get
\[ \Rightarrow {\rm{Profit\% }} = 56.25\% \]

Therefore, the gain percent is \[56.25\% \].

Note:
We know that the cost price is the price of an item at which an item is bought. The selling price is the price of an item at which an item is sold. If the selling price is greater than the cost price, then there is a profit. If the selling price is less than the cost price, then there is a loss. Profit or loss percentage is calculated only for the same number of items. Both the percentages are calculated over the cost price of an item.