 QUESTION

# A vendor bought 4 dozen eggs at Rs.4 each.7 of these were broken. At what price per dozen should he sell the remaining eggs so as to gain 10% on the whole?

Hint: We know that one dozen eggs contains 12 eggs. So, total eggs purchased were $12\times 4=48$ eggs. Now, in the solution, we will calculate the total cost of 48 eggs that he purchased. Following this total selling price with required profit will be calculated, which shall be used to find the new selling price of the per egg then multiplied by 12 to get the cost of a dozen eggs.

It is given in the question that the vendor purchased 4 dozen eggs. We know that 1 dozen eggs contain 12 eggs. Therefore 4 dozen eggs means $12\times 4=48$ eggs.
Now, the cost of 1 egg is given to be Rs. 4. Hence, the cost of 4 dozen eggs or 48 eggs = $Rs.4\times 48=Rs.192$ . Given that 7 eggs are broken, therefore the remaining number of eggs are $48-7=41$ . Now, the profit that the vendor wishes to earn is 10% of the cost of eggs. Therefore the selling price of the eggs should be 10% more than the total cost of eggs.
Hence, selling price of all eggs = $10%ofRs.192+Rs.192$
= $\dfrac{10}{100}\times Rs.192+Rs.192=Rs.211.2$ .

Total eggs he has left to sell = 41. Therefore, he should sell 41 eggs for Rs.211.2
Therefore, selling price of 1 egg = $Rs.\dfrac{211.2}{41}$ = Rs. 5.15

Since, we are asked to calculate the price for 1 dozen eggs.
Therefore, cost of 12 eggs = cost of 1 egg $\times 12$
= $Rs.5.15\times 12$
= Rs. 61.8

Note: In this question, the total number of eggs is 48 but 7 eggs are broken. So, left out eggs will be 41. But the point is now the vendor would bear a cost of Rs. 192 for 41 eggs. And he has to gain 10% on the cost of 48 eggs and not the cost of 41 eggs, that is $Rs.4\times 41=Rs.164$ .