Question

Jyotsana bought 400 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: We are given the cost price for a dozen eggs. So, we must first calculate the cost price for 100 eggs. Then, we can easily calculate the profit using the formula \[\text{Profit percentage}=\dfrac{\text{Profit}}{\text{Cost price}}\times 100\%\]. Now, we can calculate the selling price for 100 eggs.

Complete step by step answer:
We know that there are 12 items in a dozen. We can see it is given that Jyotsana bought a dozen eggs at Rs. 8.40.
So, we can say that the cost price of 12 eggs is Rs. 8.40.
Hence, by the concept of unitary method, we can write
Cost price of 1 egg = Rs. $\dfrac{8.40}{12}$
So, we can also write
Cost price of 100 eggs = Rs. $\dfrac{8.40}{12}\times 100$
Thus, on simplification, we get
Cost price of 100 eggs = Rs. 70
Jyotsana needs to earn a profit of 15%. This means the profit percentage is 15%.
We all know very well that the formula for profit percentage is
\[\text{Profit percentage}=\dfrac{\text{Profit}}{\text{Cost price}}\times 100\%\]
Thus, we can write that for 100 eggs,
$15\%=\dfrac{\text{Profit}}{70}\times 100\%$
On further solving this equation, we get
Profit = $\dfrac{15\times 70}{100}$
Hence, the value of profit for 100 eggs,
Profit = 10.5
We know that the profit earned is the difference between selling price and cost price. Hence,
$10.5=\text{Selling price}-70$
Thus, the value of selling price for 100 eggs is,
Selling price = 70 + 10.5 = 80.5.
Hence, Jyotsana must sell those eggs at the rate of Rs. 80.5 per hundred eggs.

Note: We must understand the concept of profit percentage. The profit percentage earned on 400 eggs will be the same as the profit percentage earned on 100 eggs. If we try to calculate the profit percentage on any random number of eggs, it will always be equal to a fixed constant value, 15% in this case.