Question

in an office 1/4 of the employees are women 2/3 of the women and 3/4 of the men are married if 3/4 of the married women and 8/9 of the married men have children then the fraction of the employees having no children among the total number of employees is

Answer 1

Answer:

3/8

Step-by-step explanation:

Hi,

Let 'x' be the total number of employees,

Total number of women are = 1/4th of total number of employees

= 1/4*x

= x/4

Remaining are men=> Total number of men are 3x/4.

Given 2/3rd of the women are married => Number of married women are

2/3*x/4 = x/6

Given 3/4th of the men are married => Number of married men are

3/4*3x/4 = 9x/16

Also, given that 3/4th of the married women have children

=> Number of married women who have children are = 3/4*x/6 = x/8

Also, given that 8/9th of the married men have children

=> Number of married men who have children are = 8/9*9/16 = x/2.

So, total number of employees who have children(Assuming there are no couple working in an office) are = x/8 + x/2

= 5x/8.

Hence the number of the employees having no children will be 3x/8.

Thus the required fraction of employees having no children among total number of employees = 3/8.

Hope, it helped !

Answer 2

Let total number of employees is X.

number of women employees is X/4

so, number of men employees is (X - X/4) = 3X/4.

a/c to question,
number of married women employees = 2/3 × number of total women employees
= 2/3 × X/4 = X/6
number of married men employees = 3/4 × number of total men employees.
= 3/4 × 3X/4 = 9X/16

number of married women employees have children = X/6 × 3/4 = X/8

number of married men employees have children = 9X/16 × 8/9 = X/2

so, total number of employees have children = X/8 + X/2 = 5x/8

so, number of employees having no children = X - 5X/8= 3x/8

hence, 3/8 employees of total having no children.