The mean salary of 20 workers is Rs10,250. If the salary of office sup

1.	The mean salary of 20 workers is Rs10,250. If the salary of office superintendent is added, the mean will increase by Rs 750. Find the salary of the office superintendent.
Answer» Mean = The sum of all observations/Total number of observations ∴ The sum of all observations = Mean x Total number of observations The mean salary of 20 workers is Rs 10,250. ∴ Sum of the salaries of 20 workers = 20 x 10,250 = Rs 2,05,000 …(i) If the superintendent’s salary is added, then mean increases by 750 new mean = 10, 250 + 750 = 11,000 Total number of people after adding superintendent = 20 + 1 = 21 ∴ Sum of the salaries including the superintendent’s salary = 21 x 11,000 = Rs 2,31,000 …(ii) ∴ Superintendent salary = sum of the salaries including superintendent’s salary – sum of salaries of 20 workers = 2, 31,00 – 2,05,000 …[From (i) and (ii)] = 26,000 ∴ The salary of the office superintendent is Rs 26,000.

The mean salary of 20 workers is Rs10,250. If the salary of office superintendent is added, the mean will increase by Rs 750. Find the salary of the office superintendent.

Answer»

Mean = The sum of all observations/Total number of observations

∴ The sum of all observations = Mean x

Total number of observations

The mean salary of 20 workers is Rs 10,250.

∴ Sum of the salaries of 20 workers = 20 x 10,250

= Rs 2,05,000 …(i)

If the superintendent’s salary is added, then mean increases by 750 new mean = 10, 250 + 750 = 11,000

Total number of people after adding superintendent = 20 + 1 = 21

∴ Sum of the salaries including the superintendent’s salary = 21 x 11,000 = Rs 2,31,000 …(ii)

∴ Superintendent salary = sum of the salaries including superintendent’s salary – sum of salaries of 20 workers

= 2, 31,00 – 2,05,000 …[From (i) and (ii)]

= 26,000

∴ The salary of the office superintendent is Rs 26,000.

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