Work Ratio Calculation: Man vs Woman Problem
This problem requires us to determine the ratio of work output between a man and a woman based on information about combined work efforts.
Understanding the Work Scenario
We are given two groups working together:
- Group 1: 9 men and 6 women
- Group 2: 1 man and 2 women
The core information is that the combined work rate of Group 1 is 6 times that of Group 2. Our objective is to find the ratio representing how much work 1 man does compared to 1 woman in the same time period.
Defining Work Rates
Let's denote:
- The work rate of 1 man per hour as '$m$'.
- The work rate of 1 woman per hour as '$w$'.
These variables represent the amount of work each individual completes in one hour.
Formulating the Equation
We can express the total work rate for each group:
- Work rate of Group 1 = $9m + 6w$
- Work rate of Group 2 = $m + 2w$
According to the problem statement, the work rate of Group 1 is 6 times the work rate of Group 2. This gives us the equation:
$$9m + 6w = 6 \times (m + 2w)$$
Solving for the Work Ratio
To find the ratio $m : w$, we solve the equation algebraically:
- Distribute the multiplier: Apply the factor of 6 to the terms in the parenthesis.
$$9m + 6w = 6m + 12w$$
- Isolate variables: Gather terms with '$m$' on one side and terms with '$w$' on the other.
$$9m - 6m = 12w - 6w$$
- Simplify: Combine like terms.
$$3m = 6w$$
- Determine the ratio: Express the relationship as a ratio '$m : w$' by dividing both sides by $w$ and then by 3.
$$\frac{m}{w} = \frac{6}{3}$$
$$\frac{m}{w} = \frac{2}{1}$$
This result indicates that a man's work rate is double that of a woman's.
Conclusion
The ratio of the work done by 1 man to that of 1 woman in a given time is $m : w$, which equals $2 : 1$.
Similar Questions
- A is three times more efficient than B and together they finish a piece of work in 30 days. In how many days can A alone finish the same work?
If machine A and B can produce 800 units in 3 hours and 8 hours, respectively, in how many hours can machine A and B working together at these constant rates produce 800 units?
Important Questions from Work Efficiency
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work further increased by 50%?
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
A and B together can do a piece of work in 4 days, B and C can do it in 6 days, A and C can do it in 8 days. Then A, B and C together can do the same work in :-
A can complete 50% of a work in 9 days and B can do 25% of the work in 9 days, if they work alone. If they work together then how much work (in percentage) can be completed in 6 days?
A is thrice as good a workman as B. C alone takes 48 days to paint a house. All three A, B and C working together take 16 days to paint the house. It will take how many days for A alone to paint the house?
