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On selling a book of Rs. $ 810 $ . Anil got a profit of $ 8\% . $ For how much did he purchase it?

Last updated date: 21st Jul 2024
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Hint: Given that the profit here earned is eight percent of the selling price, so selling price includes a hundred percent that is its cost price along with the profit percentage. Here we will use the cross- multiplication method to get the cost price of the book.

Complete step-by-step answer:
Let us assume that the cost price of the book be “x”
Given that: On selling a book of Rs. $ 810 $ . Anil got a profit of $ 8\% . $
Therefore, here selling price includes cost price plus profit percentage.
So, $ 108\% $ of “x” will be equal to Rs. $ 810 $
Frame the mathematical expression for the above word statement.
 $ \dfrac{{108}}{{100}} \times x = 810 $
Make the required term “x’ the subject moving other terms on the opposite side. When the term in the denominator is moved to the opposite side then it goes in the numerator and vice-versa
 $ x = \dfrac{{810 \times 100}}{{108}} $
Find the factors for the terms in the above expression –
 $ x = \dfrac{{3 \times 3 \times 9 \times 10 \times 25 \times 4}}{{3 \times 4 \times 9}} $
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
 $ x = 25 \times 3 \times 10 $
Simplify the above expression by finding the product of the terms.
 $ x = 750 $ Rs.
Hence, the cost price of the book is Rs. $ 750 $
So, the correct answer is “Rs. $ 750 $ ”.

Note: Always remember that the profit is always greater that the hundred percentage and always added with hundred percentage while loss is less than cost price percentage and therefore loss percentage is subtracted from hundred percentage. Percentage is the fraction expressed as the numerator upon hundred.