Question

During the launch of a new book, the publisher gave away 30 copies of the book as complimentary copies of the VIPs who were present at the launch and sold the remaining at a cost of Rs 500 each. If the total collection on that day was Rs 7,35,000, how many books were given out on that day as complimentary copies?

Answer 1

Hint:
Here, we will assume the total number of books to be some variable. We will use the given information and form a linear equation to find the remaining books. Then, we will equate the price of the remaining books with the given cost. We will then simplify it further to get the required value.

Complete Step by Step Solution:
Let the total number of books be \[x\].
Now, according to the question, it is given that:
 During the launch of a new book, the publisher gave away 30 copies of the book as complimentary copies of the VIPs who were present at the launch.
The number of books given to the VIPs \[ = 30\]
Hence, the remaining books \[ = \left( {x - 30} \right)\]
Now, the publisher sold the remaining books at a cost of \[{\rm{Rs}}500\] each.
The cost price of all the remaining books \[ = \left( {x - 30} \right) \times 500\]………………………\[\left( 1 \right)\]
The total collection on that day \[ = {\rm{Rs}}7,35,000\] …………………………\[\left( 2 \right)\]
Hence, equating equation \[\left( 1 \right)\] and \[\left( 2 \right)\], we get,
\[\left( {x - 30} \right) \times 500 = 7,35,000\]
Dividing both sides by 500, we get
\[ \Rightarrow \left( {x - 30} \right) = \dfrac{{7,35,000}}{{500}}\]
\[ \Rightarrow \left( {x - 30} \right) = 1470\]
Adding 30 on both sides, we get
\[ \Rightarrow x = 1500\]
Therefore, the total number of books that were given as complimentary copies on that day were 1500. Out of this 1500 books, 1470 of those books were sold for \[{\rm{Rs}}500\] each and 30 were given away as free complimentary copies to the VIPs.

Hence, 1500 is the required answer.

Note:
The alternate way of solving this question is that we could have let the number of books sold on that day be \[x\]
Then it is given that each book is sold for \[{\rm{Rs}}500\] each and the total collection on that day was \[{\rm{Rs}}7,35,000\]
Hence, making the linear equation in a similar manner, we will get,
\[x \times 500 = 7,35,000\]
Dividing both sides by 500,
\[ \Rightarrow x = \dfrac{{7,35,000}}{{500}} = 1470\]
Now, number of complimentary copies given to the VIPs \[ = 30\]
Therefore,
The total number of books which were given as complimentary \[ = 1470 + 30 = 1500\]
Where, 1470 of those books were sold for \[{\rm{Rs}}500\] each and 30 were given away as free complimentary copies to the VIPs.
Hence, 1500 is the required answer.