There are 50 paisa coins and 25 paisa coins in a bag, the total coins are 99 and their values is 33.50, then the number of each type of coins separately, is

Options

A. 35,64
B. 30, 69
C. 40, 59
D. 45, 54

Answer

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

### Step 1: Define Variables
Let:
- \( X \) = number of 50 paisa coins
- \( Y \) = number of 25 paisa coins

### Step 2: Set Up Equations
From the problem, we have two pieces of information:
1. The total number of coins is 99:
\[ X + Y = 99 \quad \text{(Equation 1)} \]
2. The total value of the coins is 33.50 rupees, which is equivalent to 3350 paisa:
\[ 50X + 25Y = 3350 \quad \text{(Equation 2)} \]

### Step 3: Simplify Equation 2
To make calculations easier, we can simplify Equation 2 by dividing everything by 25:
\[ 2X + Y = 134 \quad \text{(Equation 3)} \]

### Step 4: Solve the System of Equations
Now we have the following system of equations:
1. \( X + Y = 99 \) (Equation 1)
2. \( 2X + Y = 134 \) (Equation 3)

We can solve these equations by elimination or substitution. Let's subtract Equation 1 from Equation 3:
\[ (2X + Y) - (X + Y) = 134 - 99 \]
This simplifies to:
\[ 2X - X = 35 \]
Thus, we find:
\[ X = 35 \]

### Step 5: Find Y
Now that we have \( X \), we can substitute it back into Equation 1 to find \( Y \):
\[ 35 + Y = 99 \]
Subtracting 35 from both sides gives:
\[ Y = 99 - 35 = 64 \]

### Step 6: Conclusion
Thus, the number of each type of coin is:
- Number of 50 paisa coins (X) = 35
- Number of 25 paisa coins (Y) = 64

### Final Answer
The number of 50 paisa coins is 35, and the number of 25 paisa coins is 64.

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