The monthly salary of Shahid and Kareena together is $28,000. The salary of Shahid and Kareena is increased by `25%` and `12.5%` respectively then the new salary of Kareena becomes `120%` of the new salary of Shahid. The new (or increased) salary of Shahid is :

Options

A. 15000
B. 18000
C. 14000
D. 16000

Answer

To solve the problem, we need to find the new salary of Shahid after the given percentage increases in their salaries. Let's break down the steps:

### Step 1: Define the Salaries
Let Shahid's original salary be \( S \) and Kareena's original salary be \( K \). According to the problem, we know:
\[ S + K = 28,000 \]

### Step 2: Calculate the Increased Salaries
Shahid's salary is increased by 25%, and Kareena's salary is increased by 12.5%. Therefore:
- Shahid's new salary \( S' = S + 0.25S = 1.25S \)
- Kareena's new salary \( K' = K + 0.125K = 1.125K \)

### Step 3: Set Up the Relationship Between New Salaries
We are given that Kareena's new salary is 120% of Shahid's new salary:
\[ K' = 1.2 \times S' \]

Substituting the expressions for \( K' \) and \( S' \):
\[ 1.125K = 1.2 \times 1.25S \]
\[ 1.125K = 1.5S \]

### Step 4: Express K in Terms of S
From the equation \( 1.125K = 1.5S \), we can express \( K \) in terms of \( S \):
\[ K = \frac{1.5S}{1.125} \]
\[ K = \frac{1.5S \times 8}{9} \]
\[ K = \frac{12S}{9} \]
\[ K = \frac{4S}{3} \]

### Step 5: Substitute K Back into the Total Salary Equation
Now, substitute \( K \) back into the total salary equation:
\[ S + \frac{4S}{3} = 28,000 \]
To combine these, convert \( S \) to a fraction:
\[ \frac{3S}{3} + \frac{4S}{3} = 28,000 \]
\[ \frac{7S}{3} = 28,000 \]

### Step 6: Solve for S
Now, multiply both sides by 3:
\[ 7S = 84,000 \]
Now, divide by 7:
\[ S = 12,000 \]

### Step 7: Calculate Shahid's New Salary
Now that we have Shahid's original salary, we can find his new salary:
\[ S' = 1.25S = 1.25 \times 12,000 = 15,000 \]

### Final Answer
The new salary of Shahid is **$15,000**.

---