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A bakery shop bakes breads with the expectation that it will earn a profit of 40% on selling each loaf of bread at its

Expert replies
by Mikrislac » Fri Jul 31, 2020 3:53 pm

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Difficulty

A bakery shop bakes breads with the expectation that it will earn a profit of 40% on selling each loaf of bread at its marked price. Unfortunately during transportation of the loaves of breads to a store, 16% of the loaves were completely damaged and could not be sold. Of the remaining loaves, 24% were slightly damaged and could only be sold at 80% of their price. The final remaining loaves were sold at their marked price. What was the total profit expressed in percentage terms that the bakery shop earned in the entire transaction?

A. 2.4

B. 2.8

C. 3.2

D. 3.6

E. 4.2
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Source: — Problem Solving |

Let the total number of bread = n
Let the cost price of 1 bread = x
Let marked price/selling price = y


Loaves of bread that was completely damaged = 16%
Loaves of bread that were slightly damaged = 24%
Loaves of bread that were in good order = 100% - (16 + 24)%
= 100 - 40 = 60%


Expected profit = 40%
Completely damaged bread could not be sold while slightly damaged, bread was sold for 80% of x = 0.8x
Marked price/selling price = cost price + profit
= x + 40% of x
x + 0.4x = 1.4x
y = 1.4x


Total selling price considering the completely damaged , slightly damaged and no damage bread
Total selling price = [(16% of n) * 0] + [(24% of n) * 0.8x] + [(60% of n) * 1.4x]
= (0.24n * 0.8x) + (0.60n * 1.4x)
= 0.192nx + 0.84nx
Total selling price = 1.032nx

Total cost price = number of bread * cost of 1 bread
Total cost price = nx
Profit = total selling price - total cost price
Profit = 1.032nx - nx
Profit = 0.032nx

% profit = profit/total cost price * 100/1
% profit = 0.032nx/nx * 100/1
% profit = 3.2

Answer = C
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