Question

A manufacturing unit gives a total average salary of Rs. 100 per day to its salesman and supervisors. The average salary for a salesman per day is Rs. 85 and a company employs 440 salesman, how many supervisors does the company employed?
Statement 1: The average salary of a supervisor is Rs. 160 per day
Statement 2: The ratio between the average salaries of salesman and supervisor is 17 : 32

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is D

To determine the number of supervisors employed by the company, we need to utilize the given data and statements to form equations and solve them. 

Let's define:

• \(S_m\) as the number of salesmen, which is given as 440.
• \(S_p\) as the number of supervisors.
• \(\bar{x}_m = 85\) as the average salary of a salesman.
• \(\bar{x}_p\) as the average salary of a supervisor.
• The total average salary given is Rs. 100 per day.

We use the formula for total average salary:

\(\frac{S_m \cdot \bar{x}_m + S_p \cdot \bar{x}_p}{S_m + S_p} = 100\)

Substitute the known values:

\(\frac{440 \cdot 85 + S_p \cdot \bar{x}_p}{440 + S_p} = 100\)

This is our main equation. Let's evaluate the two statements one by one:

Statement 1:

The average salary of a supervisor is Rs. 160 per day. (\(\bar{x}_p = 160\))

Substituting in the main equation:

\(\frac{440 \cdot 85 + S_p \cdot 160}{440 + S_p} = 100\)

Solving this equation:

\(440 \cdot 85 + 160 \cdot S_p = 100 \cdot (440 + S_p)\)

\(37400 + 160S_p = 44000 + 100S_p\)

\(60S_p = 6600\)

\(S_p = 110\)

Thus, Statement 1 alone is sufficient to find the number of supervisors.

Statement 2:

The ratio between the average salaries of salesman and supervisor is 17:32.

So,

\(\frac{\bar{x}_m}{\bar{x}_p} = \frac{17}{32}\)

Substitute \(\bar{x}_m = 85\) into the ratio:

\(\frac{85}{\bar{x}_p} = \frac{17}{32}\)

Solve for \(\bar{x}_p\):

\(\bar{x}_p = \frac{85 \cdot 32}{17} = 160\)

This result is the same as \(\bar{x}_p\) in Statement 1.

Therefore, Statement 2 alone also provides enough data to find \(S_p\), and hence it is sufficient.

Conclusion: Either statement (1) alone or statement (2) alone is sufficient to determine the number of supervisors employed by the company. Therefore, the correct answer is:

 

Either statement (1) alone or statement (2) alone is sufficient to answer the question