There are some 50 paisa and some 25 paisa coins in a ba. If the total number of coins is 30 and their total value is Rs. 11, find the number of coins of each kind.

Answer

To solve the problem step by step, we will define the variables, set up equations based on the information given, and then solve those equations.

### Step 1: Define the Variables
Let:
- \( x \) = number of 50 paisa coins
- \( y \) = number of 25 paisa coins

### Step 2: Set Up the Equations
From the problem, we know:
1. The total number of coins is 30:
\[ x + y = 30 \quad \text{(Equation 1)} \]
2. The total value of the coins is Rs. 11, which is equal to 1100 paisa (since 1 Rs = 100 paisa):
\[ 50x + 25y = 1100 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
We can simplify Equation 2 by dividing the entire equation by 25:
\[ 2x + y = 44 \quad \text{(Equation 3)} \]

### Step 4: Solve the Equations
Now we have two equations:
1. \( x + y = 30 \) (Equation 1)
2. \( 2x + y = 44 \) (Equation 3)

We can solve these equations simultaneously. Let's subtract Equation 1 from Equation 3:
\[ (2x + y) - (x + y) = 44 - 30 \]
This simplifies to:
\[ 2x - x = 14 \]
\[ x = 14 \]

### Step 5: Substitute the Value of \( x \) Back into Equation 1
Now that we have \( x \), we can find \( y \) using Equation 1:
\[ 14 + y = 30 \]
\[ y = 30 - 14 \]
\[ y = 16 \]

### Conclusion
Thus, the number of coins is:
- Number of 50 paisa coins (\( x \)) = 14
- Number of 25 paisa coins (\( y \)) = 16