Out of their respective monthly salaries, Sonia and Tina spend `76%` and `68%` on various household expenses. The sum of remaining salary with Sonia and Tina together is ₹18,560. If Tina’s salary is `30%` less than that of Sonia’s, what is Tina’s monthly salary?

Options

A. ₹ 28,000
B. ₹ 29,000
C. ₹ 25,000
D. ₹ 30,000

Answer

To solve the problem step by step, we will denote Sonia's salary as \( S \) and Tina's salary as \( T \).

### Step 1: Express Tina's salary in terms of Sonia's salary
Given that Tina’s salary is 30% less than Sonia’s salary, we can express Tina's salary as:
\[ T = S - 0.3S = 0.7S \]

**Hint:** Use the percentage decrease formula to express one variable in terms of another.

### Step 2: Calculate the remaining salaries after expenses
Sonia spends 76% of her salary on expenses, which means she has:
\[ \text{Remaining salary of Sonia} = S - 0.76S = 0.24S \]
Tina spends 68% of her salary on expenses, so she has:
\[ \text{Remaining salary of Tina} = T - 0.68T = 0.32T \]

**Hint:** Calculate the remaining salary by subtracting the percentage spent from the total salary.

### Step 3: Substitute Tina's salary into the remaining salary equation
Now, substituting \( T = 0.7S \) into the equation for Tina's remaining salary:
\[ \text{Remaining salary of Tina} = 0.32T = 0.32(0.7S) = 0.224S \]

**Hint:** Substitute known values into equations to express everything in terms of one variable.

### Step 4: Set up the equation for the total remaining salary
The sum of the remaining salaries of Sonia and Tina is given as ₹18,560:
\[ 0.24S + 0.224S = 18560 \]
Combining the terms:
\[ 0.464S = 18560 \]

**Hint:** Combine like terms to simplify the equation.

### Step 5: Solve for Sonia's salary
Now, solve for \( S \):
\[ S = \frac{18560}{0.464} \approx 40000 \]

**Hint:** Use division to isolate the variable you want to solve for.

### Step 6: Calculate Tina's salary
Now that we have Sonia's salary, we can find Tina's salary using the relationship established earlier:
\[ T = 0.7S = 0.7 \times 40000 = 28000 \]

**Hint:** Substitute back into the equation to find the value of the other variable.

### Final Answer
Tina's monthly salary is ₹28,000.