A box contains of 5 rupee, 2 rupee and 1 rupee coins and their values are In the ratio of `15 : 4 : 2` respectively. If there are total 112 coins, how many 2 rupee coins are there in the box?

Options

A. 32
B. 48
C. 64
D. 24

Answer

To solve the problem step by step, we will follow the given ratios and the total number of coins.

### Step 1: Understand the Ratios
The values of the coins are given in the ratio of 15:4:2. This means:
- The value of 5 rupee coins = 15 parts
- The value of 2 rupee coins = 4 parts
- The value of 1 rupee coins = 2 parts

### Step 2: Assign Variables
Let the common multiple of the ratios be \( x \). Therefore, we can express the values as:
- Value of 5 rupee coins = \( 15x \)
- Value of 2 rupee coins = \( 4x \)
- Value of 1 rupee coins = \( 2x \)

### Step 3: Calculate the Number of Coins
To find the number of coins, we need to divide the total value of each type of coin by their respective values:
- Number of 5 rupee coins = \( \frac{15x}{5} = 3x \)
- Number of 2 rupee coins = \( \frac{4x}{2} = 2x \)
- Number of 1 rupee coins = \( \frac{2x}{1} = 2x \)

### Step 4: Set Up the Equation
According to the problem, the total number of coins is 112. Therefore, we can set up the equation:
\[ 3x + 2x + 2x = 112 \]

### Step 5: Simplify the Equation
Combine like terms:
\[ 7x = 112 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 7:
\[ x = \frac{112}{7} = 16 \]

### Step 7: Find the Number of 2 Rupee Coins
Now that we have \( x \), we can find the number of 2 rupee coins:
\[ \text{Number of 2 rupee coins} = 2x = 2 \times 16 = 32 \]

### Final Answer
Thus, the number of 2 rupee coins in the box is **32**.

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