The total profit made by the student is 56.8%
The correct answer is D
Given parameters:
final price in which he book was sold = Rs.400
the first profit made by the student = 12% = 0.12
the final profit made by the student = 40% = 0.4
To find:
- the total profit of the student
To find the total profit made by the student, we have to find the initial cost price of the book.
The cost price of the book before the student made the profit of 40%.
Let this cost price = y
100%y + 40%y = 400
140%y = 400
1.4y = 400
[tex]y = \frac{400}{1.4} \\\\y = 285.71[/tex]
This cost price become the new selling price before the student made the profit of 12%.
The cost price of the book before the student made the profit of 12%.
Let this cost price = x
100%x + 12%x = 285.71
112%x = 285.71
1.12x = 285.71
[tex]x = \frac{285.71}{1.12} \\\\x = 255.1[/tex]
This is the initial cost price of the book
The total profit made by the student is calculated as;
[tex]Profit \ \%= \frac{selling \ price - cost \ price }{cost \ price} \times 100\%\\\\Profit \ \%=(\frac{400 - 255.1}{255.1} )\times 100\%\\\\Profit \ \%= 56.8\%[/tex]
Thus, the total profit made by the student is 56.8%
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