**Given Information:**
- 2 men and 7 boys can do a piece of work in 4 days.
- 4 men and 4 boys can do the same work in 3 days.

**Let's Calculate their individual Efficiency:**

To find out how long it would take one man and one boy to do the work, we need to calculate their individual efficiencies first.

Let's assume the efficiency of one man is 'm' and the efficiency of one boy is 'b'.

**Efficiency Calculation:**

From the given information, we can create the following equations:

- (2m + 7b) * 4 = 1 (Equation 1)
- (4m + 4b) * 3 = 1 (Equation 2)

Since both equations equal to 1 (which represents the whole work), we can simplify them:

- 8m + 28b = 1/4 (Equation 1 simplified)
- 12m + 12b = 1/3 (Equation 2 simplified)

**Solving the System of Equations:**

To find the values of 'm' and 'b', we can solve this system of equations using any method (substitution, elimination, or matrix).

Let's solve it using the substitution method:

From Equation 1: 8m + 28b = 1/4

Solving for 'm':
- 8m = 1/4 - 28b
- m = (1/4 - 28b)/8

Substituting the value of 'm' into Equation 2:

12((1/4 - 28b)/8) + 12b = 1/3

Simplifying and solving for 'b':
- 3(1/4 - 28b) + 12b = 1/3
- 3/4 - 84b + 12b = 1/3
- 3/4 - 72b = 1/3
- 3 - 288b = 4
- -288b = 1
- b = -1/288

Substituting the value of 'b' into Equation 1 to find 'm':

8m + 28(-1/288) = 1/4
8m - 7/72 = 1/4
8m = 1/4 + 7/72
8m = 9/36 + 7/72
8m = 25/72
m = (25/72)/8
m = 25/576

So, the efficiency of one man is 25/576 and the efficiency of one boy is -1/288.

**Calculating the Time taken by one Man and one Boy:**

To find out how long it would take one man and one boy to do the work, we can calculate their combined efficiency.

- Combined Efficiency = Efficiency of one man + Efficiency of one boy
- Combined Efficiency = (25/576) + (-1/288)
- Combined Efficiency = 23/576

Now, we can calculate the time taken by one man and one boy using their combined efficiency:

- (1/1) / (23/576) = 576/23

Therefore, it would take one man and one boy approximately

men=15daysboy=60days