In a bag, the number of Rs 10 notes, Rs 20 notes and Rs 50 notes are in the ratio 5:4:3. the total value of the notes in it is Rs 280. find the number of Rs. 10 notes in it.

Options

A. 4
B. 5
C. 3
D. 2

Explanation

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

### Step 1: Understand the Ratio
The number of Rs 10 notes, Rs 20 notes, and Rs 50 notes are in the ratio 5:4:3. This means:
- Let the number of Rs 10 notes be \(5x\)
- Let the number of Rs 20 notes be \(4x\)
- Let the number of Rs 50 notes be \(3x\)

### Step 2: Calculate the Total Value of Each Type of Note
Now, we will calculate the total value contributed by each type of note:
- The value of Rs 10 notes = \(10 \times 5x = 50x\)
- The value of Rs 20 notes = \(20 \times 4x = 80x\)
- The value of Rs 50 notes = \(50 \times 3x = 150x\)

### Step 3: Set Up the Equation for Total Value
According to the problem, the total value of all the notes is Rs 280. Therefore, we can set up the following equation:
\[ 50x + 80x + 150x = 280 \]

### Step 4: Combine Like Terms
Now, we will combine the terms on the left side of the equation:
\[ (50x + 80x + 150x) = 280x \]
So the equation becomes:
\[ 280x = 280 \]

### Step 5: Solve for \(x\)
Now, we will solve for \(x\) by dividing both sides by 280:
\[ x = \frac{280}{280} = 1 \]

### Step 6: Find the Number of Rs 10 Notes
Now that we have the value of \(x\), we can find the number of Rs 10 notes:
\[ \text{Number of Rs 10 notes} = 5x = 5 \times 1 = 5 \]

### Final Answer
The number of Rs 10 notes in the bag is **5**.

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