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The problem in the image states:

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

Let the number of 5 paise coins be \( x \) and the number of 30 paise coins be \( y \).

From the given information, we can create two equations:

1. The total number of coins is 100:
   \[
   x + y = 100
   \]

2. The total value of the coins is Rs. 22.5 (or 2250 paise):
   \[
   5x + 30y = 2250
   \]

### Solving the system of equations:

From the first equation, \( x + y = 100 \), we can express \( x \) as:
\[
x = 100 - y
\]

Substitute this into the second equation:
\[
5(100 - y) + 30y = 2250
\]
\[
500 - 5y + 30y = 2250
\]
\[
500 + 25y = 2250
\]
\[
25y = 2250 - 500
\]
\[
25y = 1750
\]
\[
y = \frac{1750}{25} = 70
\]

So, the number of 30 paise coins is \( y = 70 \).

Now, using \( x + y = 100 \), we find:
\[
x = 100 - 70 = 30
\]

### Difference between the number of 30 paise coins and 5 paise coins:
The difference is \( 70 - 30 = 40 \).

Therefore, the correct answer is **B. 40**.

Let me know if you need further clarification or additional questions.

### Follow-up Questions:
1. How would the equations change if the total value was Rs. 30 instead of Rs. 22.5?
2. What if Geetha had only 90 coins in total with the same total value?
3. Can you generalize a formula for any combination of two types of coins and total value?
4. How would the solution change if one of the coin types was 10 paise instead of 5 paise?
5. What if the total value was given in rupees with decimal points rather than in paise?

**Tip:** Always convert currency into the smallest unit (like paise in this case) to avoid dealing with fractions in calculations.

Geetha has a certain number of 5 paise coins and a certain number of 30 paise coins. In total, she has 100 coins and the total value of the coins is Rs. 22.5. What is the difference between the number of 30 paise coins and 5 paise coins with Geetha?

Learn how to solve a system of linear equations to find the number of 5 paise and 30 paise coins in a set of 100 coins, with a total value of Rs. 22.5. This problem involves substitution and basic algebra, suitable for students in Grades 8-10.

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