This problem can be solved using the concept of arithmetic sequences because the salary increases by a fixed amount (increment) every year.

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Assumptions:

1. Let the initial salary be $S$ (in Rs.).
2. Let the yearly increment be $I$ (in Rs.).

We know:

• After 4 years, the salary becomes $15000$.
• After 10 years, the salary becomes $18000$.

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Formulating equations:

1. Salary after $n$ years: $S_n = S + n \cdot I$

2. Given conditions:

   • For $n = 4$: S + 4 \cdot I = 15000 \tag{1}
   • For $n = 10$: S + 10 \cdot I = 18000 \tag{2}

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Solving the equations:

Subtract equation (1) from equation (2): $(S + 10I) - (S + 4I) = 18000 - 15000$ $6I = 3000$ $I = 500$

Substitute $I = 500$ into equation (1): $S + 4 \cdot 500 = 15000$ $S + 2000 = 15000$ $S = 13000$

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Results:

1. Initial salary (S): Rs. 13,000 per year.
2. Yearly increment (I): Rs. 500 per year.

To find the monthly salary: $\text{Monthly salary} = \frac{\text{Yearly salary}}{12} = \frac{13000}{12} \approx 1083.33$

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Final Answer:

• Initial monthly salary: Rs. 1083.33
• Yearly increment: Rs. 500

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Would you like a detailed explanation of any step?
Here are some related questions you might find helpful:

1. What if the salary increase was not constant?
2. How would this change if increments were every 6 months instead of yearly?
3. Can you plot the salary progression over time?
4. What is the salary after 15 years?
5. How do arithmetic sequences apply to financial growth problems?

Tip: Arithmetic sequences are widely used in financial calculations like loans, savings, and salary projections. Understanding them helps in planning finances better!