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 analyze the given information step-by-step to find the total number of projects handled by Company B across all three years (2015, 2016, and 2017).

Step 1: Define variables for the year 2015
Let the number of projects handled by Company B in 2015 be $x$.
According to the question, in 2015, total projects handled by Company A are 1.5 times that of B.
So, projects handled by Company A in 2015 = $1.5x$.

Step 2: Express projects for 2016 and 2017
In 2016:
Projects handled by Company A in 2016 = $20$
Projects handled by Company B in 2016 = $x+9$

In 2017:
Projects handled by Company A in 2017 is 25% more than that of B in 2015:
$1.25x$
Projects handled by Company B in 2017 = $30$

Step 3: Solve for $x$ using the total projects handled by A
The total number of projects handled by Company A in all three years is 42.
$\left(\text{A in 2015}\right)+\left(\text{A in 2016}\right)+\left(\text{A in 2017}\right)=42$

$1.5x+20+1.25x=42$

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

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

Divide by 2.75:
$x=\frac{22}{2.75}=8$

Step 4: Calculate the total projects handled by Company B in all 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 = $30$

Total projects handled by B in all three years:
$8+17+30=55$

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