Salaries of A, B and C were in the ratio 3 : 5 : 7, respectively. If their salaries were increased by `50%, 60% and 50%` respectively, what will be the new ratio of the their respective new salaries?

Options

A. `4 : 5 : 7`
B. ` 3 : 6 : 7`
C. ` 4 : 15 : 18`
D. ` 9 : 16 : 21 `

Answer

To find the new ratio of the salaries of A, B, and C after their respective increases, we can follow these steps:

### Step 1: Define the original salaries
Let the original salaries of A, B, and C be represented as:
- Salary of A = 3x
- Salary of B = 5x
- Salary of C = 7x

### Step 2: Calculate the new salaries after the increments
Now, we will calculate the new salaries after the specified percentage increases:
- A's salary increases by 50%:
\[ \text{New Salary of A} = 3x + 0.5 \times 3x = 3x + 1.5x = 4.5x \]

- B's salary increases by 60%:
\[ \text{New Salary of B} = 5x + 0.6 \times 5x = 5x + 3x = 8x \]

- C's salary increases by 50%:
\[ \text{New Salary of C} = 7x + 0.5 \times 7x = 7x + 3.5x = 10.5x \]

### Step 3: Form the new ratio of the salaries
Now we can form the new ratio of their salaries:
\[ \text{New Ratio} = \text{New Salary of A} : \text{New Salary of B} : \text{New Salary of C} = 4.5x : 8x : 10.5x \]

### Step 4: Simplify the ratio
To simplify the ratio, we can eliminate \(x\) from all terms:
\[ 4.5 : 8 : 10.5 \]

Next, we can multiply each term by 2 to eliminate the decimal:
\[ (4.5 \times 2) : (8 \times 2) : (10.5 \times 2) = 9 : 16 : 21 \]

### Final Answer
Thus, the new ratio of their respective new salaries is:
\[ \text{New Ratio} = 9 : 16 : 21 \]

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