Question

if 40% of the male employees are replaced by female employees in an office , there should be 60% more than females than males what is the percentage of employees are females initially ?​

Answer 1

The initial percentage of females was 55%.

Given,

40% of the male employees are replaced by female employees in an office

There should be 60% more females than males now

To Find,

Initial percentage of females

Solution,

Let the initial percentage of females be 'x'

Thus, the initial percentage of males be (100 - x)

According to the question,

40% of (100 - x) are replaced by females

$\frac{40}{100}$ * (100 - x) are replaced by females

(40 - 0.4x) are replaced by females

Final percentage of males = (100 - x) - (40 - 0.4x)

Final percentage of males = (60 - 0.6x)

Final percentage of females = x + (40 - 0.4x)

Final percentage of females = (40 + 0.6x)

Now, it has been given that

(40 + 0.6x) = 60% of (60 - 0.6x) + (60 - 0.6x)

(40 + 0.6x) = $\frac{60}{100}$ * (60 - 0.6x) + (60 - 0.6x)

(40 + 0.6x) = 0.6 * (60 - 0.6x) + (60 - 0.6x)

(40 + 0.6x) = (36 - 0.36x) + (60 - 0.6x)

(40 + 0.6x) = (96 - 0.42x)

(1.02)x = 56

x = $\frac{56}{1.02}$

x ≈ 55%

Thus, the initial percentage of females was 55%.

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Answer 2

Concept:

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given:

1. 40% of the male employees are replaced by female employees.

2. There should be 60% more females than males.

Find:

We are asked to find the percentage of employees are females initially.

Solution:

We have,

40% of the male employees are replaced by female employees.

Now,

Let,

Percentage of females = x%,

So,

Percentage of males = (100 - x)%

According to the question,

Now,

40% of males are replaced by females,

i.e.

40% of (100 - x)%  = 40 - 0.4x %,

So,

Percentage of males = (100 - x) - (40 - 0.4x) = (60 - 0.6x) %

Now,

Percentage of females = x + (40 - 0.4x) = 40 + 0.6x

Now,

According to the question,

i.e.

There should be 60% more females than males.

i.e.

Percentage of females =  60% (Percentage of males ) + Percentage of males

i.e.

40 + 0.6x = 60% × (60 - 0.6x) + (60 - 0.6x)

on simplifying we get,

40 + 0.6x = 36 - 0.36x + 60 - 0.6x

i.e.,

0.6x + 0.6x + 0.36x  = 60 + 36 - 40

i.e.

1.56x = 56

So,

x = 56 / 1.56 = 35.89%

Hence, the initial percentage of employees of females was 35.89%.

#SPJ1