A bag contains 1 rupee, 50 paise and 25 paise coins. The value of 1 rupee, 50 paise and 25 paise coins are in the ratio of `5 : 3 : 1` respectively. If total number of coins is 180, what will be the total value (in Rs.) of all coins?

Options

A. 112
B. 180
C. 196
D. 108

Answer

To solve the problem step by step, let's break down the information given and find the total value of the coins in the bag.

### Step 1: Understand the Ratios
The values of the coins are given in the ratio of 5:3:1 for 1 rupee, 50 paise, and 25 paise coins respectively.

### Step 2: Assign Variables
Let the values of the coins be:
- Value of 1 rupee coins = 5x
- Value of 50 paise coins = 3x
- Value of 25 paise coins = 1x

### Step 3: Calculate Total Value
The total value of the coins can be expressed as:
\[ \text{Total Value} = 5x + 3x + 1x = 9x \]

### Step 4: Convert Values to Coins
Now, we need to convert these values into the number of coins. The values in rupees are:
- 1 rupee = 100 paise
- 50 paise = 50 paise
- 25 paise = 25 paise

Now, we can find the number of coins based on their values:
- Number of 1 rupee coins = \( \frac{5x}{1} = 5x \) coins
- Number of 50 paise coins = \( \frac{3x}{0.5} = 6x \) coins
- Number of 25 paise coins = \( \frac{1x}{0.25} = 4x \) coins

### Step 5: Total Number of Coins
The total number of coins can be expressed as:
\[ \text{Total Coins} = 5x + 6x + 4x = 15x \]

### Step 6: Set Up the Equation
We know from the problem that the total number of coins is 180. Thus, we can set up the equation:
\[ 15x = 180 \]

### Step 7: Solve for x
To find x, divide both sides by 15:
\[ x = \frac{180}{15} = 12 \]

### Step 8: Calculate the Total Value
Now, we can substitute x back into the total value equation:
\[ \text{Total Value} = 9x = 9 \times 12 = 108 \]

### Step 9: Convert to Rupees
Since the total value is in paise, we convert it to rupees:
\[ \text{Total Value in Rs.} = \frac{108}{100} = 1.08 \]

### Final Answer
The total value of all the coins in the bag is **Rs. 1.08**.

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