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Let's break down and solve the problem presented in the image:

### Problem Details:
- **Siya** has Rs. 84 in her purse, composed of Rs. 2 and Rs. 5 coins.
- **Riya** has Rs. 85 in her purse, and she has a total of 36 coins consisting of Re. 1 and Rs. 2 coins in the ratio of 5:6.

### Questions to Answer:
1. **(a)** What is the number of 2 Rupee coins in Siya's purse?
2. **(b)** Who is having a greater number of coins?
3. **(c)** Write the equation for finding the number of 2 Rupee and 5 Rupee coins in Siya's purse.
   - OR: Write the equation for finding the total number of coins in Riya's purse.

### Solution:

#### Part (a): Number of Rs. 2 Coins in Siya's Purse
Let's assume:
- The number of Rs. 2 coins in Siya's purse = \( x \)
- The number of Rs. 5 coins in Siya's purse = \( y \)

We know that:
\[ 2x + 5y = 84 \]
To answer this, we'll need the relation between \( x \) and \( y \). We'll derive this in Part (c).

#### Part (b): Who Has a Greater Number of Coins?
Let's first find the total number of coins each has:
- **Riya's total number of coins:** Given as 36 coins.
- **Siya's total number of coins:** \( x + y \)

Since we know Riya has 36 coins, once we derive the values for \( x \) and \( y \) for Siya, we can compare them directly.

#### Part (c): Equations for the Coins
For Siya, we have the equation derived from the total amount:
\[ 2x + 5y = 84 \]
This equation gives a relationship between the number of Rs. 2 and Rs. 5 coins in Siya's purse.

For Riya, since the ratio of the number of Re. 1 to Rs. 2 coins is 5:6, let's assume:
- The number of Re. 1 coins = \( 5k \)
- The number of Rs. 2 coins = \( 6k \)

Then:
\[ 5k + 6k = 36 \quad \Rightarrow \quad 11k = 36 \quad \Rightarrow \quad k = \frac{36}{11} \]
Calculating \( k \):
\[ k \approx 3.27 \]

So, the number of Re. 1 coins \( = 5 \times 3.27 \approx 16.35 \), and Rs. 2 coins \( = 6 \times 3.27 \approx 19.62 \).

However, since \( k \) must be a whole number, it seems there may be a mistake in the given problem's ratio or coin count, as 36 is not exactly divisible by 11. If \( k \) were exact, we would calculate as above.

#### Answer:
1. To determine the exact number of Rs. 2 coins in Siya's purse, we must solve the equation from part (c). 
2. **Riya** has a greater number of coins (as 36 is given), but to compare with Siya, we need exact values for \( x \) and \( y \).
3. **Equation for Siya**: \( 2x + 5y = 84 \).
   **Equation for Riya**: \( 5k + 6k = 36 \).

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Would you like more detailed calculations, or do you have further questions? Here are some related problems:

1. What if Siya had 10 more coins, how would it affect the number of Rs. 2 coins?
2. Can you find another ratio that divides 36 coins more evenly?
3. How would the problem change if Riya had Rs. 86 instead of Rs. 85?
4. What is the total value of Rs. 5 coins in Siya's purse?
5. How many more coins would Siya need to match the number of coins in Riya's purse?

**Tip:** Always verify the consistency of ratios and total counts when solving problems involving them.

Siya and Riya were going to the market to purchase some toys. Siya had Rs. 84 in her purse while Riya had Rs. 85. Siya had a total of 36 coins of Rs. 2 and Rs. 5. Riya had Re. 1 and Rs. 2 coins in the ratio 5:6. Answer the following questions: a) What is the number of 2 Rupee coins in Siya's purse? b) Who is having a greater number of coins? c) Write the equation for finding the number of 2 Rupee and 5 Rupee coins in Siya's purse or write the equation for finding the total number of coins in Riya's purse.

This problem involves solving a system of equations to find the distribution of Rs. 2 and Rs. 5 coins in Siya's purse and the coin ratio for Riya. Learn how to apply algebraic methods to answer questions about total coins and their values.

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