CAT 2008 — DILR Question 8
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 departement-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.
There are limited numbers 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.
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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?
Answer & solution
- A
30
- B
35
40
- D
45
- E
Cannot be determined
Let the age of the employee being transferred from the
1. Marketing department to the Finance department be x.
2. Finance department to the Marketing department be y.
3. Marketing department to the HR department be z.
Now,
The sum of the ages of all employees in Finance originally was 30 × 20 = 600. Later, an employee of x years of age joined the department and one of y years of age left it.
So, the new average age for the Finance department = = 31 (given)
∴ 600 + x – y = 620
∴ x – y = 20 … (i)
The sum of the ages of all employees in Marketing originally was 35 × 30 = 1050.
Later, two employees of x years and z years of age left the department and one of y years of age joined it. Since 2 employees left and 1 joined, hence the number of employees currently in this department is 29
So, the new average age for the Marketing department = . = 35 (given)
∴ 1050 – x + y – z = 1015
∴ x – y + z = 35 … (ii)
From equations (i) and (ii), we get,
20 + z = 35
∴ z = 15
The sum of the ages of all employees in HR originally was 45 × 5 = 225.
Later, one employee of z years of age joined the department. Also, the number of employees increases by one to 6.
So, the new average age for the HR department =
Hence, option (c).