A bag contains 50 P, 25P and 10 P coins in the ratio 5 : 9 : 4 amounting to Rs 206 Find the number of coins of each type .

Answer

To solve the problem step by step, we will follow the given information and use algebra to find the number of coins of each type.

### Step 1: Understand the Ratios
The coins are in the ratio of 50 paisa : 25 paisa : 10 paisa = 5 : 9 : 4.

### Step 2: Assign Variables
Let:
- The number of 50 paisa coins = 5x
- The number of 25 paisa coins = 9x
- The number of 10 paisa coins = 4x

### Step 3: Convert Total Amount to Paisa
The total amount is Rs. 206. Since 1 Rs = 100 paisa, we convert Rs. 206 to paisa:
\[ 206 \text{ Rs} = 206 \times 100 = 20600 \text{ paisa} \]

### Step 4: Write the Equation for Total Value
The total value of the coins can be expressed as:
\[ \text{Value of 50 paisa coins} + \text{Value of 25 paisa coins} + \text{Value of 10 paisa coins} = 20600 \text{ paisa} \]
This can be written as:
\[ (5x \times 50) + (9x \times 25) + (4x \times 10) = 20600 \]

### Step 5: Simplify the Equation
Calculating the values:
\[ 250x + 225x + 40x = 20600 \]
Combine like terms:
\[ 515x = 20600 \]

### Step 6: Solve for x
To find x, divide both sides by 515:
\[ x = \frac{20600}{515} = 40 \]

### Step 7: Find the Number of Coins
Now we can find the number of coins of each type:
- Number of 50 paisa coins:
\[ 5x = 5 \times 40 = 200 \]
- Number of 25 paisa coins:
\[ 9x = 9 \times 40 = 360 \]
- Number of 10 paisa coins:
\[ 4x = 4 \times 40 = 160 \]

### Final Answer
- Number of 50 paisa coins = 200
- Number of 25 paisa coins = 360
- Number of 10 paisa coins = 160

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