Final answer:
B, 35 days. By setting up and solving a system of algebraic equations based on the given information about men and boys completing work, we can determine that one man alone would take 35 days to finish the assigned work.
Step-by-step explanation:
The correct answer is option B, which is 35 days. To solve this problem, let's use algebra to find the rate at which one man or one boy can do the work. If 3 men and 4 boys can do the work in 14 days, we can write this as an equation: 3m + 4b = 1/14. Similarly, if 4 men and 6 boys can do the same work in 10 days, we write it as 4m + 6b = 1/10. We now have a system of equations that we can solve simultaneously to find the values of m (one man's work per day) and b (one boy's work per day).
After solving the system, we would find the reciprocal of m to determine how many days one man alone would take to complete the work. In this particular problem, after calculating the values, we find that it takes one man 35 days to complete the same work, assuming that the efficiency of men and boys is consistent throughout.
We can solve this problem using the concept of work efficiency. Let's assume that one man can complete the work in 'x' days.
From the given information:
3 men and 4 boys can finish the work in 14 days. This means that the total work done in 14 days is equivalent to the work done by 3 men and 4 boys in one day.
4 men and 6 boys can finish the same work in 10 days. This means that the total work done in 10 days is equivalent to the work done by 4 men and 6 boys in one day.
Let's calculate the comparative efficiency of men and boys:
In 14 days, 3 men and 4 boys complete the work, so 3 men and 4 boys can complete 1/14th of the work in one day.
In 10 days, 4 men and 6 boys complete the work, so 4 men and 6 boys can complete 1/10th of the work in one day.
Now, let's calculate the efficiency of one man compared to one boy:
Let's assume one man's efficiency is 'm' and one boy's efficiency is 'b'.