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The price of a pen is 2 times the price of a pencil. The price of a book is 10 times the price of pencil. A student bought 5 pencil, 10 pens and 2 books from a shop for rupees 135.

The problem is asking about the total cost of 5 pencils, 10 pens, and 2 books given certain relationships between their prices and the total amount paid by the student.

Let the price of a pencil be \( x \) rupees.

From the information provided:
- The price of a pen is 2 times the price of a pencil, so the price of a pen = \( 2x \).
- The price of a book is 10 times the price of a pencil, so the price of a book = \( 10x \).

The student buys:
- 5 pencils, costing \( 5x \) in total.
- 10 pens, costing \( 10 \times 2x = 20x \) in total.
- 2 books, costing \( 2 \times 10x = 20x \) in total.

The total cost is given as 135 rupees:
\[
5x + 20x + 20x = 135
\]
\[
45x = 135
\]
\[
x = \frac{135}{45} = 3
\]

Thus, the price of a pencil is \( 3 \) rupees.

- The price of a pen is \( 2 \times 3 = 6 \) rupees.
- The price of a book is \( 10 \times 3 = 30 \) rupees.

### Summary:
- Price of a pencil: 3 rupees.
- Price of a pen: 6 rupees.
- Price of a book: 30 rupees.

Would you like more details or have any questions?

Here are 5 related questions:
1. What would be the total cost if the student bought 3 pencils, 5 pens, and 1 book?
2. How much more would the student pay if the price of the pencil increased by 1 rupee?
3. If the student bought 4 more pens, how much would the total cost increase?
4. What would be the total cost if the prices of all items were doubled?
5. How would the equation change if the price of the book were 8 times the price of the pencil instead?

**Tip**: When solving word problems, always start by defining variables for the unknown quantities to make equations easier to form and solve.

The price of a pen is 2 times the price of a pencil. The price of a book is 10 times the price of pencil. A student bought 5 pencils, 10 pens and 2 books from a shop for ₹135.

Learn how to calculate the price of pencils, pens, and books using linear equations. The problem involves a student buying 5 pencils, 10 pens, and 2 books, with total cost given. Ideal for Grades 6-8.

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