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.

Projects handles by A in 2016 is how much percentage more or less than the projects handle by B in 2015?

Correct Answer: The correct option is 150%.

Step-by-Step Explanation:

Let's organize the given information step-by-step to find the required values for Company A and Company B for each year (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 problem, in 2015, the total projects handled by Company A are 1.5 times those handled by Company B.
Therefore, projects handled by Company A in 2015 = $1.5x$.

Step 2: Use the information for the years 2016 and 2017.
- In 2016, Company A handled 20 projects.
- In 2017, the projects handled by Company A are 25% more than those handled by Company B in 2015.
25% more than $x$ is equal to:
$x+0.25x=1.25x$

Step 3: Calculate the total projects handled by Company A across all three years.
The total projects handled by Company A in all three years (2015, 2016, and 2017) is given as 42.
$\left(\text{Projects by A in 2015}\right)+\left(\text{Projects by A in 2016}\right)+\left(\text{Projects by A in 2017}\right)=42$

Substitute the expressions into the equation:
$1.5x+20+1.25x=42$

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

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

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

So, the number of projects handled by Company B in 2015 is 8.

Step 4: Answer the specific question.
We need to find how much percentage more or less the projects handled by Company A in 2016 are compared to the projects handled by Company B in 2015.
- Projects handled by Company A in 2016 = 20
- Projects handled by Company B in 2015 = 8

Difference = $20-8=12$

Percentage more =
$\left(\frac{12}{8}\right)\times 100\%=1.5\times 100\%=150\%$

Therefore, projects handled by A in 2016 are 150% more than the projects handled by B in 2015.