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Answer the following question based on the information given below.

There are $100$ employees in an organization across five departments. The following table gives the department-wise distribution of average age, average basic pay and allowances. The gross pay of an employee is the sum of his/her basic pay and allowances.

 Department Number of Employees Average Age (years) Average Basic Pay (Rs) Allowances (% of Basic Pay) HR 5 45 5000 70 Marketing 30 35 6000 80 Finance 20 30 6500 60 Business Development 35 42 7500 75 Maintenance 10 35 5500 50

There are limited number of employees considered for transfer/promotion across departments. Whenever a person is transferred/promoted from a department of lower average age to a department of higher average age, he/she will get an additional allowance of $10\%$ of basic pay over and above his/her current allowance. There will not be any change in pay structure if a person is transferred/promoted from a department with higher average age to a department with lower average age.

There was a mutual transfer of an employee between Marketing and Finance departments and transfer of one employee from Marketing to HR. As a result the average age of Finance department increased by one year and that of Marketing department remained the same. What is the new average age of HR department?

1. $30$
2. $35$
3. $40$
4. $45$
5. cannot be determined

Since the average age of finance department increased by $1$, the total age became $31*20=620.$

Initially total age $= 30*20=600.$

Therefore there is a net increase of age by $20$ years. Hence the decrease in total age of Marketting department will be also $20.$ But since average age of marketing department is not changed , therefore-

total age after transfer from marketting to HR dept $= 29*35=1015.$

Initial total $= 30*35=1050.$

Decrease in total due to transfer from marketing to Finance dept $=20$. But total has to be maintained at $1015.$

Therefore HR dept age total must have been increased by $35-20=15.$

Hence new average of HR $= 45*5+15=240.$

Average $= \frac{240}{6} = 40$

Answer$: \text{C}$
by
214 points

Ma,am In finance there is Increement of One Employee followed by decreement of one in Marketing ,

But at the same time there is also increement of One Employee in HR (but there is no decreement in any other department )

simultaneously exchange between marketing and finance department so that finance department its avg age increase 1 year and marketing  dept. 20 years decrease from its total sum years (but both dept have same no. of employees). After that 1 employee transfer from marketing to HR dept.Now marketing  dept have 29 employees and its avg age remain unchanged.