Four books and eight pens were bought for Rs. 260. If the average price of a book is Rs. 35, then the average price of a pen would be:
Rs. 15
Understanding the Problem: Finding the Average Price of a Pen
The problem asks us to find the average price of a pen, given the total cost of a certain number of books and pens, and the average price of a book. We are given the following information:
- Number of books bought: 4
- Number of pens bought: 8
- Total cost of 4 books and 8 pens: Rs. 260
- Average price of a book: Rs. 35
We need to calculate the average price of a pen.
Step-by-Step Calculation of Pen's Average Price
To find the average price of a pen, we first need to find the total cost of all the pens. We can do this by subtracting the total cost of the books from the total cost of both books and pens.
Calculating the Total Cost of Books
We know the number of books and the average price per book. The total cost of the books is the number of books multiplied by the average price of one book.
Total cost of books = Number of books $\times$ Average price per book
Total cost of books = $4 \times \text{Rs. } 35$
Total cost of books = Rs. $140$
| Item | Quantity | Average Price (Rs.) | Total Cost (Rs.) |
|---|---|---|---|
| Book | 4 | 35 | $4 \times 35 = 140$ |
Calculating the Total Cost of Pens
The total cost of books and pens together is Rs. 260. We have just calculated the total cost of the books is Rs. 140. So, the total cost of the pens will be the total combined cost minus the total cost of the books.
Total cost of pens = Total cost of books and pens - Total cost of books
Total cost of pens = Rs. $260 - \text{Rs. } 140$
Total cost of pens = Rs. $120$
| Description | Cost (Rs.) |
|---|---|
| Total cost of books and pens | 260 |
| Total cost of books | 140 |
| Total cost of pens | $260 - 140 = 120$ |
Calculating the Average Price of a Pen
We now know the total cost of the pens (Rs. 120) and the number of pens bought (8). The average price of a pen is the total cost of pens divided by the number of pens.
Average price of a pen = Total cost of pens $\div$ Number of pens
Average price of a pen = Rs. $120 \div 8$
Average price of a pen = Rs. $15$
Therefore, the average price of a pen is Rs. 15.
Final Answer Determination
Based on our calculations, the average price of a pen is Rs. 15.
Revision Table: Average Price Calculation Summary
| Item | Quantity | Average Price (Rs.) | Total Cost (Rs.) |
|---|---|---|---|
| Book | 4 | 35 (Given) | $4 \times 35 = 140$ |
| Pen | 8 | 15 (Calculated) | $8 \times 15 = 120$ |
| Total | $140 + 120 = 260$ (Matches Given Total) |
Additional Information: Understanding Average Price
The average price is calculated by dividing the total cost of a group of items by the number of items in that group. It represents a typical or central value for the price of a single item in the group.
The formula for average price is:
$$ \text{Average Price} = \frac{\text{Total Cost}}{\text{Number of Items}} $$
In this problem, we used this concept in reverse to find the total cost of books (Average Price $\times$ Number of Items) and then used it directly to find the average price of pens (Total Cost of Pens $\div$ Number of Pens).
Understanding how total cost, quantity, and average price relate is crucial for solving such problems.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
