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The average price of 16 different books is Rs. 18. While the average price of 14 of these books is Rs. 16.50 and of the remaining two books, if the price of one is 50% of the other, then the price of these two books is (in rupees)
1. 13, 26
2. 17, 34
3. 19, 38
4. 21, 42

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Correct Answer - Option 3 : 19, 38

Given:

Average price of 16 books = Rs. 18

Average price of 14 books = Rs. 16.50

Price of one of remaining book = 50% of price of another remaining book

Concept used:

Average = Total sum of observation/Number of observations

Calculation:

As we know that

Average = Total sum of observation/Number of observations

Total price of 16 books = Rs. 18 × 16

⇒ Rs. 288

Total price of 14 books = Rs. 16.50 × 14

⇒ Rs. 231

Total Price of remaining books = Total price of 16 books - Total price of 14 books

⇒ Rs. (288 - 231)

⇒ Rs. 57

Now, Let the price of one of remaining book be x

Price of another remaining book = 50% of x

⇒ x/2

According to the question

x + (x/2) = Rs. 57

⇒ 3x/2 = 57

⇒ x = (57 × 2)/3

⇒ x = Rs. 38

Price of another remaining book = 38/2

⇒ Rs. 19

∴ The prices of books are Rs. 19 and Rs. 38. 

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