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's break down the information step-by-step to find the required ratio.

Step 1: Define variables for the number of projects handled by company B in 2015
Let the number of projects handled by company B in 2015 be $x$.

Step 2: Express the projects handled by company A in terms of $x$
From the given information:
- In 2015, company A handled 1.5 times the projects of company B in 2015:

$A_{2015}=1.5x$

- In 2016, company A handled 20 projects:

$A_{2016}=20$

- In 2017, company A handled 25% more projects than company B in 2015:

$A_{2017}=x+0.25x=1.25x$

Step 3: Solve for $x$ using the total projects handled by company A
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 values in terms of $x$ into the equation:

$1.5x+20+1.25x=42$

Simplify the equation:

$2.75x+20=42$

Subtract 20 from both sides:

$2.75x=22$

Divide by 2.75:

$x=\frac{22}{2.75}=8$

Thus, the projects handled by company B in 2015 is:

$B_{2015}=8$

And the projects handled by company A in 2017 is:

$A_{2017}=1.25\times 8=10$

Step 4: Find the projects handled by company C in 2015
The projects handled by company C in 2015 is 50% more than the projects handled by company A in 2017:

$C_{2015}=10\times 1.50=15$

Step 5: Calculate the required ratio
The ratio of projects handled by company B in 2015 to projects handled by company C in 2015 is:

$B_{2015}:C_{2015}=8:15$