20 men can complete a work in 10 days and x women can complete the same work in 10 days. Ratio of efficiency of man to efficiency of woman is 3:2. Find the value of x?
Question
20 men can complete a work in 10 days and x women can complete the same work in 10 days. Ratio of efficiency of man to efficiency of woman is 3:2. Find the value of x?
Solution
Let's assume that the efficiency of one man is represented by the variable "m" and the efficiency of one woman is represented by the variable "w".
Given that the ratio of the efficiency of a man to a woman is 3:2, we can write the equation:
m/w = 3/2
Now, we know that 20 men can complete the work in 10 days. This means that the total efficiency of the men is 20 times the efficiency of one man. Similarly, x women can complete the work in 10 days, so the total efficiency of the women is x times the efficiency of one woman.
Using the formula Efficiency = Work/Time, we can set up the following equations:
20m = 1 (since the work is completed in 10 days) xm = 1 (since the work is completed in 10 days)
Simplifying these equations, we get:
m = 1/20 w = 1/x
Substituting the values of m and w into the ratio equation, we have:
(1/20)/(1/x) = 3/2
Simplifying further, we get:
(1/20) * (x/1) = 3/2
Cross-multiplying, we have:
x/20 = 3/2
Multiplying both sides by 20, we get:
x = (3/2) * 20
Simplifying, we find:
x = 30
Therefore, the value of x is 30.
Similar Questions
A group of 12 persons containing men and women can do a piece of work in 13 days, other group of 10 persons containing men and women can do the same piece of work in 16 days. Number of men in first group is 1 more than the number of men in second group. If there is another group of 2 men and 6 women which can do the same piece of work in 26 days. What is the ratio of efficiency of 1 man to that of 1 woman?
8 men and 4 boys can finish a piece of work in 5 days. 6 women and 8 boys can finish the same work in 5 days. Also, 4 men and 6 women can finish the same work in 5 days. In how many days can 2 men, 3 women and 10 boys finish the same work at their double efficiency?
10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work
Four men and two women can do a piece of work together in one day. If a woman is twice as efficient as a man, in how many days can a woman working alone do the work?
8 men and 2 women together can finish a piece of work in 24 days. In how much time will 40 men and45 women together complete 1.5 times the work, if the work done by 16 men in 8 hours is equal to thework done by 2 women in 24 hours?Question 1Answera.10b.9c.3d.6
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.