Sushma joins a job at the age of 20 years. For the first 3 years, her salary is ₹10,000 per annum. After that, her salary increases by ₹2,000 every year for the next 10 years, and then the salary becomes constant until retirement. If her average salary over her entire career is ₹25,000 per annum, at what age does Sushma retire?

Introduction:
This is an “average over a career” problem combining a fixed salary period, an increment period (arithmetic progression), and then a constant salary period. The main idea is: average salary = (total earnings over all years) / (number of years). So we compute total earnings for the known parts, represent the unknown constant-salary years using a variable, and then solve using the given average salary ₹25,000 per annum. Finally, add the total career years to the starting age (20) to get the retirement age.

Given Data / Assumptions:

• Starting age = 20 years
• Years 1 to 3 salary = ₹10,000 per annum
• Next 10 years salary increases by ₹2,000 each year
• After that, salary is constant (equals salary after increments end)
• Average salary over entire career = ₹25,000 per annum

Concept / Approach:
Total earnings = sum of salary each year. Use arithmetic series sum for the 10 increment years. Let total career length be N years, then total earnings = 25,000 * N and solve for N.

Step-by-Step Solution:
First 3 years total = 3 * 10,000 = 30,000Increment period is 10 years: salaries are 12,000, 14,000, ..., up to 30,000This is an arithmetic series with first term 12,000, last term 30,000, number of terms 10Sum = (first + last) / 2 * terms = (12,000 + 30,000) / 2 * 10Sum = 42,000 / 2 * 10 = 21,000 * 10 = 210,000Total for first 13 years = 30,000 + 210,000 = 240,000After 13 years, salary becomes constant at 30,000 per yearLet total career length = N years, remaining years = N - 13Total earnings = 240,000 + 30,000*(N - 13)Average condition: 240,000 + 30,000*(N - 13) = 25,000*N240,000 + 30,000N - 390,000 = 25,000N30,000N - 150,000 = 25,000N5,000N = 150,000 => N = 30 yearsRetirement age = 20 + 30 = 50 years

Verification / Alternative check:
If N=30, total earnings should be 25,000*30=750,000. Our earnings: 240,000 + 30,000*(17) = 240,000 + 510,000 = 750,000. Matches exactly.

Why Other Options Are Wrong:
42, 45, 47: imply shorter career lengths that would produce a lower average because many early years are below 25,000.52: implies a longer career which would push the average closer to 30,000, not stay at 25,000.

Common Pitfalls:
Not treating the 10 years as an arithmetic series and summing incorrectly.Using increment for more than 10 years or ending at the wrong last salary.Forgetting that retirement age = start age + total career years.

Final Answer:
50 years