Shaan got a total of Rs. 912 in the denomination of equal numbers of Rs. 1, Rs. 5 and Rs. 10 coins. How many coins do Shaan posses?

Options

A. 16
B. 57
C. 171
D. 323

Answer

To solve the problem, we will break it down step by step.

### Step 1: Define the variables
Let the number of coins of each denomination (Rs. 1, Rs. 5, and Rs. 10) be represented by \( x \). Since Shaan has equal numbers of each type of coin, he has:
- \( x \) coins of Rs. 1
- \( x \) coins of Rs. 5
- \( x \) coins of Rs. 10

### Step 2: Calculate the total value of the coins
The total value contributed by each type of coin can be calculated as follows:
- Value from Rs. 1 coins: \( 1 \times x = x \)
- Value from Rs. 5 coins: \( 5 \times x = 5x \)
- Value from Rs. 10 coins: \( 10 \times x = 10x \)

### Step 3: Write the equation for total value
The total value of all the coins is given as Rs. 912. Therefore, we can write the equation:
\[ x + 5x + 10x = 912 \]

### Step 4: Simplify the equation
Combine the terms on the left side:
\[ 16x = 912 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 16:
\[ x = \frac{912}{16} \]
Calculating this gives:
\[ x = 57 \]

### Step 6: Calculate the total number of coins
Since Shaan has \( x \) coins of each denomination and there are three denominations, the total number of coins is:
\[ 3x = 3 \times 57 = 171 \]

### Final Answer
Shaan possesses a total of **171 coins**.

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