The average salary of all the associates in a team is Rs. 16000. The average salary of 7 senior associates is Rs. 24000 and the average salary of the rest is Rs. 12000. How many associates work in that team?

Options

A. a) 21
B. b) 22
C. c) 23
D. d) 24

Answer

To solve the problem step by step, we need to find out how many associates work in the team based on the given average salaries.

### Step 1: Define Variables
Let \( N \) be the total number of associates in the team.

### Step 2: Calculate Total Salary of All Associates
The average salary of all associates is Rs. 16,000. Therefore, the total salary of all associates can be expressed as:
\[ \text{Total Salary of All Associates} = N \times 16000 \]

### Step 3: Calculate Total Salary of Senior Associates
The average salary of 7 senior associates is Rs. 24,000. Thus, the total salary of the senior associates can be calculated as:
\[ \text{Total Salary of Senior Associates} = 7 \times 24000 = 168000 \]

### Step 4: Calculate Total Salary of Remaining Associates
The average salary of the remaining associates (those who are not senior) is Rs. 12,000. Let \( R \) be the number of remaining associates. Since there are 7 senior associates, we have:
\[ R = N - 7 \]
The total salary of the remaining associates can be expressed as:
\[ \text{Total Salary of Remaining Associates} = R \times 12000 = (N - 7) \times 12000 \]

### Step 5: Set Up the Equation
Now we can set up the equation based on the total salary of all associates:
\[ N \times 16000 = 168000 + (N - 7) \times 12000 \]

### Step 6: Expand and Simplify the Equation
Expanding the right side:
\[ N \times 16000 = 168000 + 12000N - 84000 \]
Combining like terms:
\[ N \times 16000 = 12000N + 84000 \]

### Step 7: Rearrange the Equation
Rearranging the equation gives:
\[ 16000N - 12000N = 84000 \]
\[ 4000N = 84000 \]

### Step 8: Solve for \( N \)
Dividing both sides by 4000:
\[ N = \frac{84000}{4000} = 21 \]

### Conclusion
Thus, the total number of associates in the team is \( N = 21 \).

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