Question

A serial book was published at \[{{7}^{th}}\] year intervals. When the \[{{7}^{th}}\] book was published the total sum of publication year was 13524. First book was published in
(a) 1911
(b) 1910
(c) 2002
(d) 1932

Answer 1

Hint: Consider ‘x’ as the year in which \[{{1}^{st}}\] book was published. Add 7 to each year to get the publishing year. The sum of all 7 published gives the publication of 13524. Hence solve the equation formed and get the value of x.

Complete step by step solution:
It is said that a serial book was published at an interval of 7 years. Now let us assume that the first book was published in year ‘x’. Books are published at an interval of 7 years.
\[{{1}^{st}}\] book was published in year = x
\[{{2}^{nd}}\] book was published in year = x + 7
\[{{3}^{rd}}\] book was published in year = x + 14
\[{{4}^{th}}\] book was published in year = x + 21
\[{{5}^{th}}\] book was published in year = x + 28
\[{{6}^{th}}\] book was published in year = x + 35
\[{{7}^{th}}\] book was published in year = x + 42
When the \[{{7}^{th}}\] book was issued, the sum of the publication year was 13, 524.
\[\therefore \] The sum of the publications of all 7 books = 13524.
\[\begin{align}
  & x+\left( x+7 \right)+\left( x+14 \right)+\left( x+21 \right)+\left( x+28 \right)+\left( x+35 \right)+\left( x+42 \right)=13524 \\
 & \therefore 7x+147=13524 \\
\end{align}\]
Let us simplify the above and find the value of x.
\[\begin{align}
  & \therefore 7x=13524-147 \\
 & 7x=13377 \\
 & \therefore x=\dfrac{13377}{7}=1911 \\
\end{align}\]
Hence the first book was published in the year 1911.
\[\therefore \] Option (a) is the correct answer.

Note: The question might be a little confusing when you read at first. Total publications is the total number of books or printed copies of the serial published. The number of printed copies of the 7 books is 13524. Thus solve the problem by keeping these points in mind. One might think that the answer should be a multiple of 7 and using this concept, they can eliminate the options. But doing this will not ease things because all options except (b) are divisible by 7. This method should not be adopted and the traditional method must be followed.