The text in the image reads:

"A person starts a job with some fixed salary and yearly increment. After 4 years, his yearly salary is ₹5000, and after 10 years, his salary becomes ₹7500."

This problem involves arithmetic progression. Let us analyze it:

Problem Breakdown:

1. Let the initial yearly salary (fixed salary) be S.
2. Let the yearly increment be I.
3. After 4 years, the salary will be: $S + 4I = 5000$
4. After 10 years, the salary will be: $S + 10I = 7500$

Solving the Equations:

We have two equations:

1. $S + 4I = 5000$
2. $S + 10I = 7500$

Subtracting the first equation from the second: $(S + 10I) - (S + 4I) = 7500 - 5000$ $6I = 2500$ $I = \frac{2500}{6} = 416.67$

Substituting $I = 416.67$ into $S + 4I = 5000$: $S + 4(416.67) = 5000$ $S + 1666.67 = 5000$ $S = 5000 - 1666.67 = 3333.33$

Final Answer:

• Initial salary, $S = ₹3333.33$
• Yearly increment, $I = ₹416.67$

Would you like a detailed explanation or graph? Let me know!

Related Questions:

1. How can you calculate the salary after 15 years using this formula?
2. What is the formula for the salary after $n$ years in this scenario?
3. How would the solution change if the yearly increment was fixed at $₹500$?
4. Can we calculate the total income earned over the first 10 years?
5. What are some practical uses of arithmetic progression in salary modeling?

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