The salaries of A, B and C are in the ratio `1:3:4`. If the salaries are Increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio

Options

A. `20 : 66 : 95`
B. `21 : 66 : 95`
C. `21 : 66 : 92`
D. `19 : 66 : 92`

Answer

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

### Step 1: Define the Salaries
Let the salaries of A, B, and C be represented as:
- Salary of A = 1x
- Salary of B = 3x
- Salary of C = 4x

### Step 2: Calculate the Increased Salaries
Now we will calculate the increased salaries based on the given percentage increases.

1. **For A**:
- Increase = 5% of 1x = (5/100) * 1x = 0.05x
- New Salary of A = 1x + 0.05x = 1.05x

2. **For B**:
- Increase = 10% of 3x = (10/100) * 3x = 0.3x
- New Salary of B = 3x + 0.3x = 3.3x

3. **For C**:
- Increase = 15% of 4x = (15/100) * 4x = 0.6x
- New Salary of C = 4x + 0.6x = 4.6x

### Step 3: Write the New Salaries
Now we have the new salaries:
- New Salary of A = 1.05x
- New Salary of B = 3.3x
- New Salary of C = 4.6x

### Step 4: Express the New Salaries in a Common Form
To find the ratio, we can express these salaries without the variable x:
- New Salary of A = 1.05
- New Salary of B = 3.3
- New Salary of C = 4.6

### Step 5: Convert to a Ratio
To convert these to a ratio, we can multiply each term by 100 to eliminate the decimals:
- A: 1.05 * 100 = 105
- B: 3.3 * 100 = 330
- C: 4.6 * 100 = 460

Thus, the ratio becomes:
- A : B : C = 105 : 330 : 460

### Step 6: Simplify the Ratio
Now we need to simplify the ratio:
- Divide each term by 5:
- A: 105 / 5 = 21
- B: 330 / 5 = 66
- C: 460 / 5 = 92

So, the simplified ratio is:
- 21 : 66 : 92

### Final Answer
The increased salaries of A, B, and C will be in the ratio **21 : 66 : 92**.

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