Question

A shopkeeper bought 6 dozen eggs at the rate of Rs.50 per dozen. On the way to the shop, 6 eggs broke. At what rate per egg does he need to sell the remaining to make a profit of 10%?

Answer 1

Hint: The price in which the product is bought by the seller is known as the cost price of the product, and the price in which the seller sells the product to the consumer is known as selling of the product for the seller. If the selling price of the product is greater than the cost price of the product, then the difference in the prices can be termed as the profit or the gain on the product while at the same time if the selling price is less than the cost price of the product, then the difference in the price is known as the loss on the product. Profit percent or loss percent of a product is always calculated on the cost price of the product.

Complete step-by-step answer:
In this question, the cost per dozen eggs is given, find the cost of all eggs that the shopkeeper bought, and then find the selling price of eggs that were sold for 10% profit, then find the selling price of the remaining eggs.
Price of per dozen eggs= Rs.50
Therefore, the Cost Price for 6 dozen eggs\[ = 50 \times 6 = Rs.300\]
Now, 6 of the eggs got broken by the shopkeeper, so the number of eggs left with him \[ = \left( {6 \times 12} \right) - 6 = 72 - 6 = 66eggs\]
The selling price of the eggs if all eggs were sold at 10% profit
 \[
  P\% = \dfrac{{SP - CP}}{{CP}} \times 100 \\
  \dfrac{{10}}{{100}} = \dfrac{{SP}}{{CP}} - 1 \\
  \dfrac{{SP}}{{CP}} = 0.1 + 1 \\
  SP = 1.1 \times 300 \\
  SP = Rs.330 \\
 \]
Therefore the selling price of each egg of remaining 66eggs \[ = \dfrac{{330}}{{66}} = Rs.5\]
Hence the cost of each eggs for which shopkeeper must sell the eggs to gain 10% profit =Rs.5

Note: Students can solve this question by finding the cost of each egg where cost price and selling price at 10% profit can be calculated taking 1 egg into consideration.