Each question below is followed by two Statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer
What is the salary of B, in a group of A, B, C and D whose average salary is Rs. 62880?
I. Total of the salaries of A and C is exact multiple of 10
II. Average of the salaries of A, C and D is Rs. 61665.

Options

A. if the Statement I alone is sufficient to answer the question but the Statement II alone is not sufficient
B. if the Statement II alone is sufficient to answer the question but the Statement I alone is not sufficient
C. if both Statement I and II together are needed to answer the question
D. if either the Statement I alone or Statement II alone is to sufficient to answer the question

Answer

To determine the salary of B in the group of A, B, C, and D, we need to analyze the information provided in the statements.

**Given:**
- The average salary of A, B, C, and D is Rs. 62880.

**Step 1: Calculate the total salary of A, B, C, and D.**
- Since the average salary is Rs. 62880, we can find the total salary by multiplying the average by the number of individuals (4 in this case):

\[ \text{Total Salary} = \text{Average Salary} \times \text{Number of Individuals} = 62880 \times 4 = 251520 \]

**Step 2: Analyze Statement I.**
- Statement I states that the total of the salaries of A and C is an exact multiple of 10.

Let’s denote:
- Salary of A = A
- Salary of C = C
- Salary of B = B
- Salary of D = D

From Statement I, we have:

\[ A + C = 10k \quad \text{(for some integer k)} \]

However, this information alone does not provide us with any specific value or relationship that allows us to determine B's salary. Therefore, Statement I alone is **not sufficient** to answer the question.

**Step 3: Analyze Statement II.**
- Statement II states that the average of the salaries of A, C, and D is Rs. 61665.

Using this information, we can calculate the total salary of A, C, and D:

\[ \text{Total Salary of A, C, and D} = \text{Average Salary} \times \text{Number of Individuals} = 61665 \times 3 = 184995 \]

**Step 4: Calculate the salary of B.**
- Now we can find B's salary using the total salaries calculated:

\[ B = \text{Total Salary of A, B, C, D} - \text{Total Salary of A, C, D} \]

Substituting the values we found:

\[ B = 251520 - 184995 = 66525 \]

Thus, we have determined that the salary of B is Rs. 66525.

**Conclusion:**
- Statement I is not sufficient to determine B's salary.
- Statement II is sufficient to determine B's salary.

The answer is that **Statement II alone is sufficient to answer the question, while Statement I alone is not sufficient.**

**Final Answer: Option 2.**

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