In a certain office, 1/3 of workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of the workers are without children?
Question
In a certain office, 1/3 of workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of the workers are without children?
Solution
Let's break this down:
- 1/3 of the workers are women, which means 2/3 of the workers are men.
- 1/2 of the women are married and 1/3 of these married women have children. This means 1/2 * 1/3 = 1/6 of the women have children.
- Since 1/3 of the workers are women, this means 1/3 * 1/6 = 1/18 of the workers are women with children.
- 3/4 of the men are married and 2/3 of these married men have children. This means 3/4 * 2/3 = 1/2 of the men have children.
- Since 2/3 of the workers are men, this means 2/3 * 1/2 = 1/3 of the workers are men with children.
- Adding the fractions of workers who are women with children and men with children, we get 1/18 + 1/3 = 7/18 of the workers have children.
- To find the fraction of workers without children, we subtract the fraction of workers with children from 1 (since all workers are either with children or without children). This gives us 1 - 7/18 = 11/18.
So, 11/18 of the workers are without children.
Similar Questions
Select the correct answerIn an office, one-third of the workers are women, half of the women are married and one third of the married women have children. If three-fourth of the men are married and one-third of the married men have children, then what is the ratio of married women to married men?Options2 : 11 : 23 : 11 : 3
In a joint family there are father, mother, 3 married sons and one unmarried daughter. Of the sons, 2 have 2 daughters each, and one has a son. How many female members are there in the family?
In an office 60% of the staff is female. 20% of the male staff and 20% of the female staffs are married. Find the percentage of unmarried staffs in the office.20%40%60%80%
If 40 men or 60 women or 80 children can do a piece of work in 6 months, then 10 men, 10 women and 10 children together do half of the work in ?
Select the correct answerStudy the following information carefully and answer the given questions.In a family there are eight members. A is mother of B, who is brother of C. C and Q are siblings. Y is daughter of P. Z is brother in law of B, who is son of D. A has only one son. There are only two married couples in the family. P is married to B. How many male members are there in the family?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.