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.

The correct answer is 55.

Let us break down the given information step-by-step to find the total number of projects handled by company B in all three years.

Step 1: Define variables for the year 2015
Let the number of projects handled by company B in 2015 be
$B_{2015}$
According to the problem statement, in 2015, the total projects handled by company A are 1.5 times those of company B. Therefore:
$A_{2015}=1.5\times B_{2015}$

Step 2: Define projects for the year 2016
In 2016, company B handles 9 more projects than it did in 2015:
$B_{2016}=B_{2015}+9$
Company A handles 20 projects:
$A_{2016}=20$

Step 3: Define projects for the year 2017
In 2017, the projects handled by company A are 25% more than those handled by company B in 2015:
$A_{2017}=B_{2015}+0.25\times B_{2015}=1.25\times B_{2015}$
Company B handles 30 projects:
$B_{2017}=30$

Step 4: Use the total projects handled by company A to solve for B₂₀₁₅
We are given that the total projects handled by company A across all three years is 42:
$A_{2015}+A_{2016}+A_{2017}=42$
Substitute the expressions we obtained for company A:
$(1.5\times B_{2015})+20+(1.25\times B_{2015})=42$
Combine the terms containing $B_{2015}$:
$2.75\times B_{2015}+20=42$
Subtract 20 from both sides:
$2.75\times B_{2015}=22$
Solve for $B_{2015}$:
$B_{2015}=\frac{22}{2.75}=8$

Step 5: Calculate the projects handled by company B in each year
Now we can compute the projects handled by company B in 2015, 2016, and 2017:
1) $B_{2015}=8$
2) $B_{2016}=8+9=17$
3) $B_{2017}=30$

Step 6: Find the total projects handled by B in all three years
Sum the projects for all three years:
$B_{\text{total}}=8+17+30=55$
Therefore, the total projects handled by company B in all three years is 55.