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

Answer

To solve the problem, we will follow these steps:

### 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. We can represent the number of each type of note using a common variable \( k \):
- Number of Rs 10 notes = \( 5k \)
- Number of Rs 20 notes = \( 4k \)
- Number of Rs 50 notes = \( 3k \)

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

### 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:
\[ 50k + 80k + 150k = 280 \]

### Step 4: Combine Like Terms
Now, we combine the terms on the left side:
\[ (50 + 80 + 150)k = 280 \]
\[ 280k = 280 \]

### Step 5: Solve for \( k \)
To find the value of \( k \), we divide both sides of the equation by 280:
\[ k = \frac{280}{280} = 1 \]

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

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

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