Question

I bought a number of books one day, four times on the next day, and eight times on the third day. In all I bought 78 books. How many books did I buy on the second day?
A) 6
B) 8
C) 16
D) 24
E) 36

Answer 1

Hint:
Here, we will assume to find the number of books bought on one day to be some variable. They will use the given information and find the books bought on the second and third day in terms of the assumed variable. We will then add the number of books obtained and equate it to the total number of books. We will solve it further to get the required number of books bought on the first day. We will then use this value to find the required answer.

Complete step by step solution:
We are given that I have bought a number of books in one day. Let $x$ be the number of books that I bought in one day.
We are given that books are bought four times on the next day and eight times on the third day. Therefore, Numbers of books bought on one day $ = x$
Numbers of books bought on the next day i.e., the second day $ = 4x$
Numbers of books bought on the third day $ = 8x$
We are given that the total number of books I bought on all these days is 78 books.
Total number of books bought on all these days $ = 78$ ……………………………………$\left( 1 \right)$
We know that the total number of books bought can be found by adding the number of books on the first day, number of books on the second day and number of books on the third day.
By substituting the number of books on the first day, the second day and on the third day in equation $\left( 1 \right)$, we get
$ \Rightarrow x + 4x + 8x = 78$
By adding the terms, we get
$ \Rightarrow 13x = 78$
Dividing both sides by 13, we get
$ \Rightarrow x = \dfrac{{78}}{{13}}$
$ \Rightarrow x = 6$
So, the number of books bought on one day $ = 6$ ,
The number of books bought on the second day $ = 4\left( 6 \right) = 24$
The number of books bought on the third day $ = 8\left( 6 \right) = 48$
Therefore the number of books that I bought on the second day is $24$.

Thus Option(D) is the correct answer.

Note:
We should remember that we are given the total number of books so that the arithmetic operation is addition. As the number of books is four times the number of books on the first day and the number of books is eight times the number of books on the first day, so, here we will use the arithmetic operation of multiplication. Here we have to find the book bought on the second day, so we should not leave the answer by just finding the number of books bought on the first day.