Directions : Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the question. Read both the statements and choose the appropriate option. Average age of employees working in a department is 30 years. In the next year, ten workers will retire. What will be the average age in the next year ? I. Retirement age is 60 years. II. There are 50 employees in the department.

### Concept & Strategy To find a new average after a population change, you must use the total sum formula. $$\text{New Average} = \frac{\text{New Total Sum}}{\text{New Number of People}}$$ We need the initial number of people to find the initial sum, and the specific ages of leaving members to adjust that sum. ### Step-by-Step Solution * **Given:** Current average = 30 years. Next year, 10 workers leave. * **Evaluating Statement I alone:** "Retirement age is 60 years." This tells us the 10 retiring workers will be 60 years old when they leave. However, without knowing the total number of employees, we cannot calculate the total sum of ages for the remaining workers. *Statement I alone is NOT sufficient.* * **Evaluating Statement II alone:** "There are 50 employees in the department." Current total sum of ages = $50 \times 30 = 1500$. Next year, before anyone retires, the total sum would be $1500 + 50 = 1550$ (everyone ages by 1 year). We know 10 people leave, so the new headcount is 40. But we don't know the ages of the 10 people leaving, so we cannot find the new total sum. *Statement II alone is NOT sufficient.* * **Evaluating Statements I and II together:** From II, next year's total sum before retirements = 1550. From I, 10 workers retire at age 60. The sum of their ages leaving the pool is $10 \times 60 = 600$. New total sum of ages = $1550 - 600 = 950$. New number of employees = $50 - 10 = 40$. New average = $\frac{950}{40}$. Since we can calculate the exact new average, both statements together are sufficient. ### Exam Strategy & Shortcut Map out the variables needed for the formula: $\text{New Avg} = \frac{\text{Old Sum} + \text{Aging} - \text{Retiring Sum}}{\text{New Headcount}}$. The prompt gives us "Old Avg" and "Retiring Headcount". We need "Old Headcount" (to get Old Sum and New Headcount) and "Retiring Age" (to get Retiring Sum). Statement I provides the Retiring Age. Statement II provides the Old Headcount. Both are strictly required. ### Common Pitfall A very common mistake is forgetting that everyone ages by 1 year "next year." Students often take the current sum (1500), subtract the retiring sum (600), and divide by 40, completely missing the $+50$ years added as the remaining staff aged. Always account for time passing for the whole group. ### Final Answer **Therefore, the correct answer is The data in both Statements I and II together are necessary to answer the question.**