CAT 2008 LRDI Question 8 · LR - Mathematical Reasoning

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 = $\frac{600+x-y}{20}$ = 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 = .$\frac{1050-x+y-z}{29}$ = 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 = $\frac{225+z}{6}=\frac{225+15}{6}=\frac{240}{6}=40$

Hence, option (c).