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?4: 15: 25: 35: 1

This problem can be solved by setting up a system of equations based on the information given in the problem.

Let's denote the work rate of a man as M and the work rate of a woman as W.

From the first piece of information, we know that a group of 12 people can complete the work in 13 days. If we denote the number of men in this group as x, then the number of women is 12 - x. Therefore, we can write the equation:

13(xM + (12 - x)W) = 1 (work)

From the second piece of information, we know that a group of 10 people can complete the work in 16 days. Since the number of men in this group is one less than in the first group, we can write the equation:

16((x - 1)M + (11 - x)W) = 1 (work)

From the third piece of information, we know that a group of 2 men and 6 women can complete the work in 26 days. Therefore, we can write the equation:

26(2M + 6W) = 1 (work)

Now we have a system of three equations with three unknowns (x, M, W). Solving this system will give us the values of x, M, and W, and therefore the ratio of the efficiency of a man to that of a woman.

This is a complex system of equations that may require the use of algebraic techniques or a computer program to solve.