Question

In the year 2013, in a company the ratio of employees in three different departments HR, MT and TA are 2:3:4 respectively. In the year 2014 in each department if 'n' number of employees left then the ratio becomes 3:5:7. In the year 2015 in each department 5 employees left then the ratio became 1:2:3. Then what is the total number of employees in the year 2014?​

Answer 1

In the year 2013, in a company the ratio of employees in three different departments HR, MT and TA are 2:3:4 respectively. In the year 2014 in each department if 'n' number of employees left then the ratio becomes 3:5:7.

Answer 2

The total number of employees in the year 2014 is 75.

Step-by-step explanation:

In the year 2013 the ratio of employees are = 2 : 3 : 4

                                                                       = 2x : 3x : 4x

in the year 2014 in each department 'n' number of employees left, then the ratio becomes = 3 : 5 : 7

                        = 3y  : 5y : 7y

In the year 2015 in each department 5 employees left, then the ratio became = 1 : 2 : 3

(3y-5) : (5y-5) : (7y-5) = 1 : 2 : 3

$\frac{3y-5}{5y-5}=\frac{1}{2}$

(3y-5) × 2 = 1 × (5y-5)

6y - 10 = 5y - 5

y - 10 = -5

y = 5

Therefore, the number of employees in 2014 = (3×5) : (5×5) : (7×5)

                                                                           = 15, 25, 35

Employees in 2013

2x - n = 15

3x - n = 25

x = 10                                

Therefore, the number of employees in 2013 = (2×10) : (3×10) : (4×10)

                                                                           = 20, 30, 40

5 employees left in 2015 = (15-5) (25-5) (35-5)

                                         = 10, 20, 30

then the ratio became 1 : 2 : 3

Hence the total number of employees in the year 2014

= 15 + 25 + 35

= 75 employees

The total number of employees in the year 2014 is 75.

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