The salaries of Radha and Sham were in the ratio 7 : 6 a year ago. Currently, each of them has received a raise of Rs 3000 and hence their salaries are now in the ratio 15 : 13. What is their combined salary (in Rupees) currently?

Let's solve the problem step by step.

### Step 1: Define the salaries a year ago
Let Radha's salary a year ago be \(7x\) and Sham's salary be \(6x\), where \(x\) is a common multiplier.

### Step 2: Account for the raises
Radha and Sham each received a raise of Rs 3000. Therefore, their current salaries are:

- Radha's current salary: \(7x + 3000\)
- Sham's current salary: \(6x + 3000\)

### Step 3: Set up the ratio equation
According to the problem, the ratio of their current salaries is now 15:13. Therefore, we can set up the following equation:

\[
\frac{7x + 3000}{6x + 3000} = \frac{15}{13}
\]

### Step 4: Cross-multiply and solve for \(x\)
Cross-multiplying gives:

\[
13(7x + 3000) = 15(6x + 3000)
\]

Expanding both sides:

\[
91x + 39000 = 90x + 45000
\]

### Step 5: Simplify the equation
Subtract \(90x\) from both sides:

\[
x + 39000 = 45000
\]

Subtract 39000 from both sides:

\[
x = 6000
\]

### Step 6: Calculate their current salaries
Now, substitute \(x = 6000\) back into the expressions for their salaries:

- Radha's current salary: \(7x + 3000 = 7(6000) + 3000 = 42000 + 3000 = 45000\) Rs
- Sham's current salary: \(6x + 3000 = 6(6000) + 3000 = 36000 + 3000 = 39000\) Rs

### Step 7: Find the combined current salary
The combined salary is:

\[
45000 + 39000 = 84000 \text{ Rs}
\]

So, their combined current salary is **Rs 84,000**.

Would you like more details or have any questions?

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**Related Questions:**

1. What was the total combined salary of Radha and Sham a year ago?
2. If they received an additional raise of Rs 2000, what would the new ratio of their salaries be?
3. How would the solution change if Sham's raise was Rs 4000 instead of Rs 3000?
4. What would Radha's salary be if the current salary ratio was 16:13 instead of 15:13?
5. How much more does Radha currently earn than Sham?

**Tip:** When dealing with ratio problems, setting up an equation by defining variables is crucial for finding the correct solution.

Learn how to solve a ratio problem involving salaries of Radha and Sham. Understand the concept of ratios, arithmetic operations, and step-by-step solution methods. Suitable for Grades 7-9.

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