Question

A bakery bakes cake with the expectation that it will earn a profit of 40% by selling each cake at marked price. But during the delivery to the showroom 16% of cakes were completely damaged and hence could not be sold. 24% of the cakes were slightly damaged and hence could be sold at 80% of the cost price. The remaining 60% of the cakes were sold at marked price. What is the percentage profit in the whole consignment?
A. 3.2
B. 2.4
C. 2.8
D. 4.2
E. 3.6

Answer 1

Hint: We will calculate Profit Percentage by using formula:
Profit Percentage = $100 \times \dfrac{Profit}{Total \ Cost \ Price}\%$
The gain or loss is always calculated on the cost price.

Complete step-by-step answer:
Let us assume that the total number of cakes baked are 100 and let the price of each cake be Rs. 100.
Then, Total Cost Price of 100 Cakes = Price of 1 cake $\times$ Total number of cakes = $100 \times 100 = 10000$ Rs.
Bakery earns a profit of 40% by selling each cake at Marked Price.
Thus, Marked Price of 1 cake = 100 + 40% of 100
Marked price of 1 cake = $100+\dfrac{40}{100}\times 100=100+40=140$ Rs.
Now, in order to calculate profit percent, we require total selling price.
We know, 24% of the cakes were slightly damaged and were sold at 80% of the cost price.
Thus, selling price of 24 cakes = 24 $\times$ 80% of 100
Selling price of 24 cakes = $24\times \dfrac{80}{100}\times 100=24 \times 80=1920$ Rs.
Also, 60% of the cakes were sold at marked price.
Thus, selling price of 60 cakes = 60 $\times$ Marked Price = 60 $\times$ 140 = 8400 Rs.
Since, 16% of the cakes were completely damaged and could not be sold, thus, the selling price of 16 cakes is 0 Rs.
Now, Total Selling price of 100 cakes = 1920 + 8400 = 10320 Rs.
Now, applying the formula of profit, we get,
Profit = Total Selling Price – Total Cost Price = 10320 – 10000 = 320 Rs.
Now, Profit Percent = $100 \times \dfrac{Profit}{Total \ Cost \ Price}=100 \times \dfrac{320}{1000}=\dfrac{32000}{10000}=3.2\%$
Hence, option A is correct.

Note: In this type of questions, we start by calculating total cost price and total selling price and then calculate profit percentage (loss percentage) by calculating the net profit (net loss).