Problem:
The cost of 30 eggs is equal to the sale price of 20 eggs. What is the percentage of profit?

Solution:

To find the percentage of profit, we need to calculate the cost price and selling price of 20 eggs.

Let the cost price of 30 eggs be x.
Then, the cost price of 1 egg = x/30.

Since the cost of 30 eggs is equal to the sale price of 20 eggs, the selling price of 20 eggs is also x.

Therefore, the selling price of 1 egg is x/20.

Profit = Selling price - Cost price
Profit = (x/20) - (x/30)
Profit = (3x - 2x)/60
Profit = x/60

Percentage of profit = (Profit / Cost price) x 100
Percentage of profit = [(x/60) / (x/30)] x 100
Percentage of profit = 50%

Explanation:

The given problem states that the cost of 30 eggs is equal to the sale price of 20 eggs. This means that the seller is earning a profit on the sale of eggs.

To find the percentage of profit, we need to first calculate the cost price and selling price of 20 eggs. We can do this by assuming the cost price of 30 eggs to be x.

We then calculate the cost price of 1 egg as x/30. Since the cost of 30 eggs is equal to the sale price of 20 eggs, we know that the selling price of 1 egg is also x/20.

We can then calculate the profit earned on the sale of 20 eggs by subtracting the cost price from the selling price. This gives us a profit of x/60.

Finally, we can calculate the percentage of profit by dividing the profit by the cost price and multiplying by 100.

In this case, we get a percentage of profit of 50%. This means that the seller is earning a profit of 50% on the sale of eggs.

Solution:

Let the cost price of one egg is Rs. x

Then the cost price of 30 eggs is Rs. 30x

Let the selling price of one egg is Rs. y

Then the selling price of 20 eggs is Rs. 20y

and the selling price of 30 eggs is Rs. 30y

By the given condition,

30x = 20y

or, 3x = 2y

or, y = 3x/2 ..... (1)

Now, profit = Rs. (30y - 30x)

= Rs. {30 (3x/2) - 30x}, by (1)

= Rs. (45x - 30x)

= Rs. 15x

∴ profit% is = profit/cost price * 100%

= 15x/(30x) * 100%

= 50%