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 one book is 60% more than the price of the other, what is the price of each of these two books?
- Rs.10, Rs.16
- Rs.12, Rs.18
- Rs.14, Rs.20
- Rs.16, Rs.24
- Rs.18, Rs.26
Correct Answer: A
Solution and Explanation
Approach Solution 1:
Given:
- The average price of 10 books is Rs.12
- The average price of 8 of these books is Rs.11.75.
Condition:
- Of the remaining two books, the price of one book is 60% more than the price of the other
Find out:
- The price of each of these two books
Total cost of 10 books = 10*12 = 120.
Total cost of 8 books = 8 * 11.75 = 94
Total cost of the remaining 2 books = 26.
NOTE: the price of one book is 60% more than the price of the other. It can be translated as follows:
Let the price of 1 book is x. Considerin this, other must be 160% of x.
160/100 * x
= 1.6x.
Hence,
x + 1.6x = 26
2.6x = 26
x = 26/2.6
x = 260 / 26.
x = 10.
The cost of a book = 10
cost of the other one = 1.6*10 = 16.
Approach Solution 2:
Given:
- The average price of 10 books is Rs.12
- The average price of 8 of these books is Rs.11.75.
Condition:
- Of the remaining two books, the price of one book is 60% more than the price of the other
Find out:
- The price of each of these two books
cost of 8 books = 11.75*8 = 94
and 2 books = 120-94 = 26
So as per the problem statement, for 2 books ; x+1.6x= 26
x= 10
and 1.6x = 16
Approach Solution 3:
Total price of the remaining two books = 10 x 12 - 8 x 11.75
= 120 - 94 = Rs 26
Suppose the price of one book = Rs x
Then, price of the other book = x + 60% of x = 160/100x= 8x/5
Given, x+8x/5= 26⇒13x/5= 26
⇒x= 26*5/13=Rs10
Therefore, price of the other book = Rs 8×10/5= Rs16
“The average price of 10 books is Rs.12 while the average price of 8 of”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018 Quantitative Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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