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 step-by-step derive the number of projects handled by companies A and B in the years 2015, 2016, and 2017 using the given information.

Step 1: Define variables for the year 2015

Let the number of projects handled by company B in 2015 be $x$.

According to the given statement, in 2015, total projects handled by company A are 1.5 times that of B.

Therefore, projects handled by A in 2015 = $1.5x$.

Step 2: Determine projects handled in 2016 and 2017

In 2016:

Projects handled by A in 2016 = $20$

Projects handled by B in 2016 = $x+9$

In 2017:

Projects handled by B in 2017 = $30$

Projects handled by A in 2017 are 25% more than that by B in 2015:

Projects handled by A in 2017 = $x+0.25x=1.25x$

Step 3: Solve for $x$ using total projects handled by A

We are given that the total projects handled by A in all three years (2015, 2016, and 2017) is 42.

$\left(\text{Projects by A in 2015}\right)+\left(\text{Projects by A in 2016}\right)+\left(\text{Projects by A in 2017}\right)=42$

$1.5x+20+1.25x=42$

$2.75x+20=42$

$2.75x=22$

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

So, the number of projects handled by B in 2015 is $x=8$.

Step 4: Calculate projects handled by A in 2017

Projects handled by A in 2017 = $1.25x=1.25\times 8=10$.

Step 5: Find projects handled by C in 2015

Projects handled by C in 2015 is 50% more than the projects handled by A in 2017:

Projects by C in 2015 = $10+0.50\times 10=15$.

Step 6: Find the required ratio

We need to find the ratio between projects handled by B in 2015 to projects handled by C in 2015:

$\text{Ratio}=\frac{\text{Projects handled by B in 2015}}{\text{Projects handled by C in 2015}}=\frac{8}{15}$

Thus, the required ratio is 8:15.