A bag contains 10 rupees, 2 rupees and 1 rupee coins. The value of 10 rupees, 2 rupees and 1 rupee coins are in the ratio of 15 : 8 : 1 respectively. If total number of coins is 273, then what will be the total value (in Rs) of all coins?

Options

A. 1008
B. 924
C. 1102
D. 1218

Answer

To solve the problem step by step, we will follow the information given in the question and the ratios provided.

### Step 1: Understand the Ratios
We know the values of the coins are in the ratio of 15:8:1 for 10 rupee, 2 rupee, and 1 rupee coins respectively.

### Step 2: Define Variables
Let:
- The value of 10 rupee coins = 15x
- The value of 2 rupee coins = 8x
- The value of 1 rupee coins = 1x

### Step 3: Total Value Calculation
The total value of all coins can be expressed as:
\[ \text{Total Value} = 15x + 8x + 1x = 24x \]

### Step 4: Relate Value to Number of Coins
Next, we relate the values to the number of coins:
- Let the number of 10 rupee coins = \( \frac{15x}{10} = \frac{3x}{2} \)
- Let the number of 2 rupee coins = \( \frac{8x}{2} = 4x \)
- Let the number of 1 rupee coins = \( \frac{1x}{1} = x \)

### Step 5: Total Number of Coins
The total number of coins is given as 273:
\[ \frac{3x}{2} + 4x + x = 273 \]

### Step 6: Simplify the Equation
To simplify, we first convert all terms to have a common denominator:
\[ \frac{3x}{2} + \frac{8x}{2} + \frac{2x}{2} = 273 \]
Combining the fractions gives:
\[ \frac{3x + 8x + 2x}{2} = 273 \]
\[ \frac{13x}{2} = 273 \]

### Step 7: Solve for x
To eliminate the fraction, multiply both sides by 2:
\[ 13x = 546 \]
Now, divide by 13:
\[ x = 42 \]

### Step 8: Calculate Total Value
Now that we have \( x \), we can find the total value:
\[ \text{Total Value} = 24x = 24 \times 42 = 1008 \]

### Final Answer
The total value of all coins is **Rs. 1008**.

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