A bag contains 50p, 25p and 10p coins. The ratio of coins is 5:9:4 and total amount is Rs 206. Then find number of coins.

Options

A. `20,36,16`
B. `150,180,80`
C. `200,360,160`
D. `75,180,160`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the problem
We have a bag containing three types of coins: 50 paisa, 25 paisa, and 10 paisa. The ratio of the number of coins is given as 5:9:4, and the total amount of money in the bag is Rs 206.

### Step 2: Convert the total amount into paisa
Since the amounts are given in rupees, we convert Rs 206 into paisa:
\[ 206 \text{ Rs} = 206 \times 100 \text{ paisa} = 20600 \text{ paisa} \]

### Step 3: Set up the variables based on the ratio
Let the number of 50 paisa coins be \(5k\), the number of 25 paisa coins be \(9k\), and the number of 10 paisa coins be \(4k\), where \(k\) is a common factor.

### Step 4: Calculate the total value of the coins
The total value in paisa can be expressed as:
\[ \text{Value from 50 paisa coins} = 5k \times 50 = 250k \text{ paisa} \]
\[ \text{Value from 25 paisa coins} = 9k \times 25 = 225k \text{ paisa} \]
\[ \text{Value from 10 paisa coins} = 4k \times 10 = 40k \text{ paisa} \]

### Step 5: Set up the equation
Now, we can set up the equation for the total value of coins:
\[ 250k + 225k + 40k = 20600 \]

### Step 6: Combine like terms
Combine the terms on the left side:
\[ (250 + 225 + 40)k = 20600 \]
\[ 515k = 20600 \]

### Step 7: Solve for \(k\)
Now, divide both sides by 515 to find \(k\):
\[ k = \frac{20600}{515} \]
\[ k = 40 \]

### Step 8: Calculate the number of coins
Now that we have \(k\), we can find the number of each type of coin:
- Number of 50 paisa coins:
\[ 5k = 5 \times 40 = 200 \]
- Number of 25 paisa coins:
\[ 9k = 9 \times 40 = 360 \]
- Number of 10 paisa coins:
\[ 4k = 4 \times 40 = 160 \]

### Step 9: Summarize the results
Thus, the number of coins of each type is:
- 50 paisa coins: 200
- 25 paisa coins: 360
- 10 paisa coins: 160

### Final Answer:
The number of coins is:
- 50 paisa: 200
- 25 paisa: 360
- 10 paisa: 160

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