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 option is 55.

Let us break down the information step-by-step to find the total projects handled by company B in all three years (2015, 2016, and 2017).

Let the number of projects handled by company A in 2015 be $A_{2015}$ and by company B in 2015 be $B_{2015}$.

From the first condition:
"In 2015, Total projects handle by A are 1.5 times of B."
This gives the equation:
$A_{2015}=1.5\times B_{2015}$

From the second condition:
"In 2016, Total project handle by B is 9 more than that of in 2015 and A handle 20 projects."
This gives:
$B_{2016}=B_{2015}+9$
$A_{2016}=20$

From the third condition:
"In 2017, total project handle by A is 25% more than that of by B in 2015 and B handle 30 projects."
This gives:
$A_{2017}=1.25\times B_{2015}$
$B_{2017}=30$

We are also given:
"Total projects handle by A in all three years is 42."
This gives:
$A_{2015}+A_{2016}+A_{2017}=42$

Now, substitute the values and expressions for A's projects in terms of $B_{2015}$ into this sum:
$(1.5\times B_{2015})+20+(1.25\times B_{2015})=42$

Simplify the equation:
$2.75\times B_{2015}+20=42$
$2.75\times B_{2015}=42-20$
$2.75\times B_{2015}=22$
$B_{2015}=\frac{22}{2.75}=8$

Now we can calculate the projects handled by company B in each of the three years:
1) In 2015: $B_{2015}=8$
2) In 2016: $B_{2016}=B_{2015}+9=8+9=17$
3) In 2017: $B_{2017}=30$

Finally, find the total projects handled by B in all three years:
$\text{Total projects for B}=B_{2015}+B_{2016}+B_{2017}$
$\text{Total projects for B}=8+17+30=55$