The information given about number of project handle by two companies (A and B) in three different years (2015, 2016 and 2017). Read the information carefully and answer the questions given below.

In 2015, Total projects handle by A are 1.5 times of B.
In 2016, Total project handle by B is 9 more than that of in 2015 and A handle 20 projects.
In 2017, total project handle by A is 25% more than that of by B in 2015 and B handle 30 projects.
Total projects handle by A in all three years is 42.

Find the total projects handle by B in all three years.

To find the total number of projects handled by company B in all three years (2015, 2016, and 2017), we can set up algebraic equations based on the given information.

Let the number of projects handled by company B in the year 2015 be $x$.

Based on the details provided in the question, we can express the number of projects for each company in each year as follows:

Year 2015:
- Projects handled by B in 2015 = $x$
- Projects handled by A in 2015 is 1.5 times that of B = $1.5x$

Year 2016:
- Projects handled by B in 2016 is 9 more than that of B in 2015 = $x+9$
- Projects handled by A in 2016 = $20$

Year 2017:
- Projects handled by A in 2017 is 25% more than that of B in 2015:
$\text{Projects by A in 2017}=x+0.25x=1.25x$
- Projects handled by B in 2017 = $30$

We are given that the total projects handled by company A in all three years is 42:
$\text{Total projects by A}=\text{Projects by A in 2015}+\text{Projects by A in 2016}+\text{Projects by A in 2017}=42$

Substituting the values we obtained above:
$1.5x+20+1.25x=42$

Combine the like terms:
$2.75x+20=42$

Subtract 20 from both sides:
$2.75x=22$

Solve for $x$:
$x=\frac{22}{2.75}=8$

Now, we can find the projects handled by company B in each of the three years:
- Projects handled by B in 2015 = $x=8$
- Projects handled by B in 2016 = $x+9=8+9=17$
- Projects handled by B in 2017 = $30$

Finally, calculate the total projects handled by company B in all three years:
$\text{Total projects by B}=8+17+30=55$

Thus, the total number of projects handled by company B in all three years is 55.