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.

The projects handle by C in 2015 is 50% more than the project handle by A in 2017. Find the ratio between projects handle by B in 2015 to projects handle by C in 2015.

The correct option is 8:15.

Let us analyze the given information step-by-step to find the number of projects handled by each company in different years.

Let the number of projects handled by company B in the year 2015 be represented by $B_{2015}$.

From the first statement, the total projects handled by company A in 2015 is 1.5 times that of company B in 2015:
$A_{2015}=1.5\times B_{2015}$

From the second statement, for the year 2016, company A handled 20 projects:
$A_{2016}=20$

From the third statement, the total projects handled by company A in 2017 is 25% more than that handled by company B in 2015:
$A_{2017}=1.25\times B_{2015}$

We are given that the total projects handled by company A in all three years (2015, 2016, and 2017) is 42:
$A_{2015}+A_{2016}+A_{2017}=42$

Substituting the expressions for A in each year into this equation:
$(1.5\times B_{2015})+20+(1.25\times B_{2015})=42$

Simplifying the equation by combining the terms with $B_{2015}$:
$2.75\times B_{2015}+20=42$
$2.75\times B_{2015}=42-20$
$2.75\times B_{2015}=22$

Solving for $B_{2015}$:
$B_{2015}=\frac{22}{2.75}=8$

Thus, company B handled 8 projects in 2015.

Now, let's find the number of projects handled by company A in 2017:
$A_{2017}=1.25\times 8=10$

We are given that the projects handled by company C in 2015 is 50% more than the projects handled by company A in 2017:
$C_{2015}=A_{2017}\times (1+0.50)$
$C_{2015}=10\times 1.5=15$

Finally, we need to find the ratio between the projects handled by company B in 2015 to company C in 2015:
$\text{Ratio}=B_{2015}:C_{2015}=8:15$

Therefore, the required ratio is 8:15.