Read the following table carefully and answer the questions given below.The table shows total number of EV manufactured by five different companies. The table also shows the percentage of petrol vehicles manufactured out of the total vehicles (diesel, EV and Petrol) manufactured and the percentage of diesel vehicles manufactured out of the total petrol vehicles manufactured by these companies.

Companies	Total EV manufactured	Percentage of petrol vehicles manufactured	Percentage of diesel vehicles manufactured
A	64	60%	40%
B	120	40%	25%
C	171	30%	75%
D	300	25%	60%
E	28	50%	80%

Find the difference between the total number of diesel vehicles manufactured by D and the total number of vehicles (diesel, EV, and petrol) manufactured by B.

The correct option is 165.

To find the difference between the total number of diesel vehicles manufactured by D and the total number of vehicles (diesel, EV, and petrol) manufactured by B, we will analyze the data step-by-step for both companies.

Let $T$ be the total number of vehicles (diesel, EV, and petrol) manufactured by a company.

From the problem statement:
- Petrol vehicles manufactured = $\text{Percentage of petrol vehicles}\times T$
- Diesel vehicles manufactured = $\text{Percentage of diesel vehicles}\times \text{Petrol vehicles manufactured}$
- EV vehicles manufactured = $T-(\text{Petrol vehicles}+\text{Diesel vehicles})$

Step 1: Calculate the total number of vehicles manufactured by B

For Company B:
- Total EV manufactured = 120
- Percentage of petrol vehicles = 40% of $T$
- Percentage of diesel vehicles = 25% of petrol vehicles

Let $T_B$ be the total vehicles manufactured by B.

$\text{Petrol vehicles}=0.40T_B$

$\text{Diesel vehicles}=0.25\times 0.40T_B=0.10T_B$

Since the total number of vehicles is the sum of EV, petrol, and diesel vehicles:
$T_B=120+0.40T_B+0.10T_B$
$T_B=120+0.50T_B$
$0.50T_B=120$
$T_B=240$

So, the total number of vehicles manufactured by B is 240.

Step 2: Calculate the total number of diesel vehicles manufactured by D

For Company D:
- Total EV manufactured = 300
- Percentage of petrol vehicles = 25% of $T$
- Percentage of diesel vehicles = 60% of petrol vehicles

Let $T_D$ be the total vehicles manufactured by D.

$\text{Petrol vehicles}=0.25T_D$

$\text{Diesel vehicles}=0.60\times 0.25T_D=0.15T_D$

Using the total sum formula:
$T_D=300+0.25T_D+0.15T_D$
$T_D=300+0.40T_D$
$0.60T_D=300$
$T_D=500$

Now, calculate the total number of diesel vehicles manufactured by D:
$\text{Diesel vehicles of D}=0.15\times 500=75$

Step 3: Find the difference

We need to find the difference between the total vehicles manufactured by B and the diesel vehicles manufactured by D:
$\text{Difference}=240-75=165$