Question

In an organization, 40% of the employees are matriculates. 50% of the remaining are graduates and the remaining 180 are post-graduates. How many employees are graduates?
a) 360 b) 240 c) 300 d) 180

Answer 1

Let, the total number of employees be,'x'

The number of matriculate employees = (x*40/100)

                                                                = 40x/100

So, the number of employees = (x-40x/100)

                                                  = (100x-40x)/100

                                                  = 60x/100

So, the number of graduate employees = (60x*50/100*100)

                                                                  = 30x/100

So, the number of post-graduate employees = (60x/100) - (30x/100)

                                                                           = (60x-30x)100

                                                                           = 30x/100

By condition,

30x/100 = 180

or, 30x = 180*100

or, x = 180*100/30

or, x = 6*100

or, x = 600

So, the number of matriculate employees = (600*40/100)

                                                                     = 6*40

                                                                     = 240 employees

So, the number of remaining employees = (600 - 240)

                                                                    = 360 employees

So, the number of graduate employees = (360*50/100)

                                                                  = (360/2)

                                                                  = 180 employees

(Ans): (d) 180 employees.

 

Answer 2

Answer:

Given,

Matriculate employees = 40% of total

graduates = 50% of remaining

post graduates = 180

To find : number of graduate employees

Explanation:

Let the total number of employees be x

matriculate = 4x/10= 2x/5

remaining =

$x - \frac{2x}{5} = \frac{5x - 2x}{5} = \frac{3x}{5}$

graduate employees = 1/2 of 3x/5

$\frac{1}{2} \times \frac{3x}{5} = \frac{3x}{10}$

number of remaining employees that are post graduates = 180

$x -( \frac{2x}{5} + \frac{3x}{10} ) \\ \frac{10x - 4x - 3x}{10} = \frac{10x - 7x}{10} \\ \frac{3x}{10}$

3x/10 = 180

x = 600

total number of employees = 600

number of graduates = 3(600)/10 = 180