A bag contains `25` paise and `50` paise coins whose total value is `Rs 30`. If the number of `25` paise coins is four times that of `50` paise coins, find the number of each type of coins.

Answer

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

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

### Step 2: Convert Total Value to Paise
The total value of the coins is given as Rs 30. Since 1 Rupee = 100 Paise, we convert Rs 30 to paise:
\[ 30 \text{ Rs} = 30 \times 100 = 3000 \text{ paise} \]

### Step 3: Set Up the First Equation
The total value of the coins can be expressed as:
\[ 25x + 50y = 3000 \]
This is our first equation.

### Step 4: Set Up the Second Equation
We are told that the number of 25 paise coins is four times that of 50 paise coins. Therefore, we can express this relationship as:
\[ x = 4y \]
This is our second equation.

### Step 5: Substitute Equation 2 into Equation 1
Now, we will substitute \( x \) from the second equation into the first equation:
\[ 25(4y) + 50y = 3000 \]
This simplifies to:
\[ 100y + 50y = 3000 \]
Combining like terms gives:
\[ 150y = 3000 \]

### Step 6: Solve for \( y \)
Now, we can solve for \( y \):
\[ y = \frac{3000}{150} = 20 \]
So, the number of 50 paise coins \( y \) is 20.

### Step 7: Solve for \( x \)
Now that we have \( y \), we can find \( x \) using the second equation:
\[ x = 4y = 4 \times 20 = 80 \]
So, the number of 25 paise coins \( x \) is 80.

### Final Answer
- The number of 25 paise coins is **80**.
- The number of 50 paise coins is **20**.

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