Let's solve this problem together.

Problem:

Geetha has a certain number of 5 paise coins and 30 paise coins. She has 100 coins in total, and the total value of the coins is Rs. 22.5. We need to find the difference between the number of 30 paise coins and 5 paise coins.

Step-by-Step Approach:

1. Let the number of 5 paise coins be $x$ and the number of 30 paise coins be $y$**.

   Given:

   • Total number of coins: $x + y = 100$ (Equation 1)
   • Total value of coins: $0.05x + 0.30y = 22.5$ (Equation 2, because 5 paise is $0.05$ Rs, and 30 paise is $0.30$ Rs)

2. Solve the system of equations:

   From Equation (1): $x = 100 - y$

   Substitute $x = 100 - y$ into Equation (2): $0.05(100 - y) + 0.30y = 22.5$ Simplify: $5 - 0.05y + 0.30y = 22.5$ $0.25y = 22.5 - 5$ $0.25y = 17.5$ $y = \frac{17.5}{0.25} = 70$

   So, the number of 30 paise coins $y = 70$.

3. Find $x$: Using Equation (1): $x = 100 - 70 = 30$

   So, the number of 5 paise coins $x = 30$.

4. Difference between the number of 30 paise coins and 5 paise coins: $y - x = 70 - 30 = 40$

Thus, the correct answer is Option B: 40.

Would you like a detailed breakdown of any step, or have more questions on related topics?

Here are some related questions for practice:

1. What is the value of Rs 1 coin if the total number of coins and value changes?
2. If there were only 50 coins in total, how would the answer change?
3. How would the solution change if the value of the coins was Rs. 30?
4. What if the difference in the number of coins was already given, how would you approach it?
5. Can you solve the same problem using substitution instead of elimination?

Tip: When solving word problems, always translate the given information into equations step by step!