Question : On selling 14 notebooks a seller makes a profit equal to the selling price of 9 notebooks. Find his percentage of profit. (The selling price of all notebooks is the same. The cost price of all notebooks is the same.)
Option 1: 210%
Option 2: 180%
Option 3: 140%
Option 4: 130%
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Correct Answer: 180%
Solution :
Given,
Notebooks sold = 14
Profit = Selling price of 9 notebooks
Selling price = Cost price + Profit and
Profit% = $\frac{\text{Profit}}{\text{Cost price}}\times 100$
Let's assume that the selling price of 1 notebook is 'SP'
and the cost price of 1 notebook is 'CP'.
⇒ The selling price of 14 notebooks = 14SP
⇒ The cost price of 14 notebooks = 14CP
According to the question:
Profit = Selling Price – Cost Price
⇒ 9SP = 14SP – 14CP
⇒ 14CP = (14 – 9)SP
⇒ 14CP = 5SP
⇒ $\frac{\text{CP}}{\text{SP}} = \frac{5}{14}$
⇒ CP = 5 units
⇒ SP = 14 units
⇒ Profit = 9 unit
Now, Profit % = $\frac{9}{5} ×$100 = 180%
Hence, the correct answer is 180%.
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