The mean salary of 20 workers is ₹10,250. If the salary of office su

1.	The mean salary of 20 workers is ₹10,250. If the salary of office superintendent is added, the mean will increase by ₹ 750. Find the salary of the office superintendent .
Answer» Mean = \(\cfrac{The\,sum \,of \,all \,observations}{Total \,number \,of \,observations}\) ∴ The sum of all observations = Mean x Total number of observations The mean salary of 20 workers is ₹ 10,250. ∴ Sum of the salaries of 20 workers = 20 x 10,250 = ₹ 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 = ₹ 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 ₹ 26,000.

The mean salary of 20 workers is ₹10,250. If the salary of office superintendent is added, the mean will increase by ₹ 750. Find the salary of the office superintendent .

Answer»

Mean = \(\cfrac{The\,sum \,of \,all \,observations}{Total \,number \,of \,observations}\)

∴ The sum of all observations = Mean x Total number of observations

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

∴ Sum of the salaries of 20 workers

= 20 x 10,250

= ₹ 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 = ₹ 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 ₹ 26,000.