A pen, pencil and an eraser together cost Rs. 21. The pen costs as much more than the pencil as the pencil does than the eraser. How much does the pencil cost?

Correct option is B

Given:

• The total cost of a pen, pencil, and eraser is Rs. 21.
• The pen costs as much more than the pencil as the pencil does than the eraser.

Formula and Concept:

1. Let the cost of:
   • The eraser = x
   • The pencil = y
   • The pen = z
2. From the problem:
   • z - y = y - x (The pen costs as much more than the pencil as the pencil does than the eraser).
   • x + y + z = 21 (The total cost of the three items).

Solution:

1. From the equation z - y = y - x:
   Rearrange to get:
   z + x = 2y.

2. Substitute z + x = 2y into x + y + z = 21:
   Replace z + x with 2y:
   2y + y = 21.

3. Simplify:
   3y = 21.
   y = 7.

4. Substitute y = 7 into z + x = 2y:
   z + x = 2(7) = 14.

5. Solve for x and z:
   Using x + y + z = 21:
   x + 7 + z = 21.
   x + z = 14.

Thus, the cost of the pencil is Rs. 7.

Final Answer:

(b) 7.