Question

A book seller bought 200 textbooks for Rs. 12,000. He wanted to sell them at a profit so that he could get 20 books free. At what profit percent should he sell them?
(a) \[10\% \]
(b) \[20\% \]
(c) \[30\% \]
(d) \[40\% \]

Answer 1

Hint: Here, we need to find the gain percent required such that the seller can get 20 books free. The cost price of the 20 books is the required profit. We will use a unitary method to find the cost of 20 books. Then, we will use the formula for gain percent to find the required gain/profit percent.

Formula Used:
We will use the formula \[{\rm{Gain Percent}} = \dfrac{{{\rm{Gain}}}}{{{\rm{C}}{\rm{.P}}{\rm{.}}}} \times 100\], where \[{\rm{C}}{\rm{.P}}{\rm{.}}\] is the cost price.

Complete step-by-step answer:
We will use unitary method to find the cost price of 20 textbooks.
It is given that the cost price of 200 textbooks is Rs. 12,000.
Therefore, we get
\[ \Rightarrow \]Cost price of 200 textbooks \[ = \] Rs. 12000
Dividing both sides of the equation by 200, we get
\[ \Rightarrow \]Cost price of 1 textbook \[ = {\rm{Rs}}{\rm{. }}\dfrac{{12000}}{{200}} = {\rm{Rs}}{\rm{. }}60\]
Finally, multiplying both sides of the equation by 20, we get
\[ \Rightarrow \]Cost price of 20 textbooks \[ = {\rm{Rs}}{\rm{. }}60 \times 20 = {\rm{Rs}}{\rm{. }}1200\]
The book seller wanted to sell the 20 books at a profit so that he get 20 books free.
Therefore, he wanted to buy the 20 books with the profit.
Thus, the required profit is equal to the cost price of 20 textbooks.
Using this, we get
Gain \[ = {\rm{Rs}}{\rm{. 1200}}\]
Finally, we will find the required profit/gain percent on the sale of the 200 textbooks.
Substituting \[{\rm{Gain}} = {\rm{Rs}}{\rm{. }}1200\] and \[{\rm{C}}{\rm{.P}}{\rm{.}} = {\rm{Rs}}{\rm{. }}12000\] in the formula \[{\rm{Gain Percent}} = \dfrac{{{\rm{Gain}}}}{{{\rm{C}}{\rm{.P}}{\rm{.}}}} \times 100\], we get
\[{\rm{Gain Percent}} = \dfrac{{1200}}{{12000}} \times 100\]
Simplifying the expression, we get
\[\begin{array}{l} \Rightarrow {\rm{Gain Percent}} = \dfrac{{120000}}{{12000}}\\ \Rightarrow {\rm{Gain Percent}} = 10\% \end{array}\]
\[\therefore \] The profit percent or gain percent required on the sale of the 200 textbooks such that the seller gets 20 books free, is \[10\% \].
Thus, the correct option is option (a).

Note: We used a unitary method to solve the problem. Unitary method is a method where first, the per unit quantity is calculated, and then the number of units are multiplied. Here, we calculated the cost price of 1 textbook and multiplied it by 20 to get the cost price of 20 textbooks. The price at which an object is bought, that price is known as cost price.