Question

The average price of 10 books is Rs.12, while the average price of 8 of these books is Rs.11.75. Of the remaining two books, if the price of the one is 60% more than the price of the other, what is the price of each of these books?
A. Rs.8, Rs.12
B. Rs.10, Rs.16
C. Rs.5, Rs.7.50
D. Rs.12, Rs.14

Answer 1

Hint: Average is the total price divided by no. of books. So using this, we find the total price for 10 books and 8 books, say x and y respectively. To find the price of the remaining 2 books, say z, subtract the price y from price x. In those 2 books one book’s price is 60% more than the price of the other. If one’s price is x then the other’s price will be $x + \dfrac{{60x}}{{100}}$. Add these two prices and equate it to z to find the price of those two books.

Complete step-by-step answer:
We are given that the average price of 10 books is Rs.12 and average of 8 of these books is Rs.1175.
We have to find the price of the remaining 2 books if the price of one is 60% more than the other.
Average of 10 books is Rs.12, this means the price of 10 books is $12 \times 10 = Rs.120$
Average of 8 of these books is Rs.11.75, this means the price of 8 books is $11.75 \times 8 = Rs.94$
Price of the remaining 2 books is $120 - 94 = Rs.26$
In these two books, the price of one is 60% more than the price of the other.
Let the price of one book is x then the price of other book will be $x + x \times \dfrac{{60}}{{100}} = x + \dfrac{{3x}}{5} = \dfrac{{8x}}{5}$
The price of these two books is Rs.26. This means,
$
   \to x + \left( {\dfrac{{8x}}{5}} \right) = 26 \\
   \to \dfrac{{5x + 8x}}{5} = 26 \\
   \to 13x = 26 \times 5 = 130 \\
   \to x = \dfrac{{130}}{{13}} \\
  \therefore x = 10 \\
  \dfrac{{8x}}{5} = \dfrac{{8 \times 10}}{5} = 16 \\
$
The price of one book is Rs.10 and the price of another book is Rs.16.
So, the correct answer is “Option B”.

Note: The average money is the ratio of total money and the total no. of books. Average is also called as mean. The units of the average will be the units of the numerator. We got a linear equation in the end. An easy approach to solve linear equations is to put all the variable terms in the LHS and all the constant terms in the RHS as we did above. Taking the percentage as decimals will be easier than taking them as fractions like 60% as 0.6.