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.

To find the required ratio, let us break down the information given for companies A and B across the years 2015, 2016, and 2017 step-by-step.

Step 1: Set up variables for projects handled in 2015
Let the number of projects handled by company B in 2015 be $x$.
According to the problem, the number of projects handled by company A in 2015 is 1.5 times that of B:
$\text{Projects handled by A in 2015}=1.5x$

Step 2: Determine projects handled in 2016
- Projects handled by B in 2016 is 9 more than in 2015: $x+9$
- Projects handled by A in 2016 = 20

Step 3: Determine projects handled in 2017
- Projects handled by A in 2017 is 25% more than that of B in 2015:
$\text{Projects handled by A in 2017}=x+0.25x=1.25x$
- Projects handled by B in 2017 = 30

Step 4: Solve for $x$ using total projects handled by A
We are given that the total projects handled by A across all three years is 42:
$\text{Projects by A in 2015}+\text{Projects by A in 2016}+\text{Projects by A in 2017}=42$

Substituting the values in terms of $x$:
$1.5x+20+1.25x=42$

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

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

Solve for $x$:
$x=\frac{22}{2.75}=\frac{2200}{275}=8$

So, the number of projects handled by company B in 2015 is:
$\text{Projects by B in 2015}=8$

Step 5: Find the projects handled by company A in 2017
Using $x=8$:
$\text{Projects by A in 2017}=1.25\times 8=10$

Step 6: Find the projects handled by company C in 2015
The projects handled by C in 2015 is 50% more than the projects handled by A in 2017:
$\text{Projects by C in 2015}=1.5\times 10=15$

Step 7: Find the required ratio
The ratio between projects handled by B in 2015 to projects handled by C in 2015 is:
$\text{Ratio}=\frac{\text{Projects by B in 2015}}{\text{Projects by C in 2015}}=\frac{8}{15}=8:15$

Therefore, the correct option is 8:15.