A bag has 840 in the denomination of rs. 1 Rs. 2 and Rs. 5 coins. Rs. 1, Rs. 2 and Rs. 5 coins are in the ratio of 8:1:5. How many coins of Rs. 5 are in the bag?

Options

A. 60
B. 24
C. 600
D. 120

Answer

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

### Step 1: Understand the Ratios
We are given that the coins of Rs. 1, Rs. 2, and Rs. 5 are in the ratio of 8:1:5. This means:
- For every 8 coins of Rs. 1, there is 1 coin of Rs. 2, and 5 coins of Rs. 5.

### Step 2: Assign Variables
Let the number of Rs. 1 coins be \(8x\), the number of Rs. 2 coins be \(1x\), and the number of Rs. 5 coins be \(5x\).

### Step 3: Calculate the Total Value
Now, we can calculate the total value of the coins:
- The value of Rs. 1 coins = \(8x \times 1 = 8x\)
- The value of Rs. 2 coins = \(1x \times 2 = 2x\)
- The value of Rs. 5 coins = \(5x \times 5 = 25x\)

Adding these values together gives us the total value:
\[ \text{Total Value} = 8x + 2x + 25x = 35x \]

### Step 4: Set Up the Equation
We know the total value of the coins is Rs. 840, so we can set up the equation:
\[ 35x = 840 \]

### Step 5: Solve for \(x\)
To find \(x\), we divide both sides of the equation by 35:
\[ x = \frac{840}{35} = 24 \]

### Step 6: Find the Number of Rs. 5 Coins
Now that we have \(x\), we can find the number of Rs. 5 coins:
\[ \text{Number of Rs. 5 coins} = 5x = 5 \times 24 = 120 \]

### Final Answer
Therefore, the number of Rs. 5 coins in the bag is **120**.

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