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Question

The average salary of all the workers in a workshop is ₹11500.
If the average salary of 5 technicians is ₹8000 and the average salary of the rest of the workers is ₹14000, then the total number of workers in the workshop is

A
11
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B
12
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C
13
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D
14
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Solution

The correct option is B 12
Let:
T = Total number of workers
ST = Sum of salaries of T workers
S5 = Sum of salaries of 5 workers
Average of numbers = Sum of numbersTotal number of numbers
∴ 11500 = Sum of total salary of workersTotal number of workers
11500=STT
ST=11500×T .........(i)
and 8000=Sum of salary of 5 workers5
S5=8000×5
S5=40000 …..(ii)
and, 14000=Sum of (T-5) workers(T-5)workers
STS5=14000×(T5) …..(iii) Substituting the values of (i) and (ii) in (iii), we get
11500×T40000=14000×(T5)
115T400=140T700
700400=140T115T
300=25T
T=12
Therefore, there are total of 12 workers in the workshop.
Hence, the correct answer is option (b).

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