The average monthly salary of the workers in a workshop is Rs. 8,500. If the average monthly salary of 7 technicians is Rs. 10,000 and the average monthly salary of the rest is Rs. 7,800, then the total number of workers in the workshop isa)18b)20c)22d)24Correct answer is option 'C'. Can you explain this answer?

Question

Answer

To find the total number of workers in the workshop, we can use the concept of weighted averages. We are given the average monthly salary of the workers in the workshop, the average monthly salary of the technicians, and the average monthly salary of the rest of the workers.

Step 1: Finding the average monthly salary of all workers
We know that the average monthly salary of the technicians is Rs. 10,000. Let's assume there are 7 technicians. So, the total salary of the technicians would be 7 x Rs. 10,000 = Rs. 70,000.

We also know that the average monthly salary of the rest of the workers is Rs. 7,800. Let's assume there are 'n' workers in this group. So, the total salary of the rest of the workers would be n x Rs. 7,800 = Rs. 7,800n.

The average monthly salary of all workers can be calculated by taking the weighted average of the average monthly salaries of the technicians and the rest of the workers.

Average monthly salary of all workers = (Total salary of technicians + Total salary of rest of workers) / Total number of workers

Rs. 8,500 = (Rs. 70,000 + Rs. 7,800n) / (7 + n)

Step 2: Solving the equation
To solve this equation, we can cross-multiply:

Rs. 8,500 x (7 + n) = Rs. 70,000 + Rs. 7,800n

59,500 + Rs. 8,500n = Rs. 70,000 + Rs. 7,800n

Rs. 8,500n - Rs. 7,800n = Rs. 70,000 - Rs. 59,500

700n = 10,500

n = 10,500 / 700

n = 15

Step 3: Finding the total number of workers
We have found that the number of workers in the rest of the group is 15. Since there are 7 technicians, the total number of workers in the workshop is 7 + 15 = 22.

Therefore, the correct answer is option C) 22.

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