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 answer is 165.

Let us define the variables for any company:
Let $T$ be the total number of vehicles (diesel, EV, and petrol) manufactured by the company.
Let $P$ be the number of petrol vehicles manufactured.
Let $D$ be the number of diesel vehicles manufactured.
Let $\text{EV}$ be the number of electric vehicles manufactured.

From the problem description:
1. Petrol vehicles manufactured ($P$) is given as a percentage of the total vehicles ($T$).
2. Diesel vehicles manufactured ($D$) is given as a percentage of the petrol vehicles ($P$).
3. The total vehicles is the sum of petrol, diesel, and electric vehicles:
$T=\text{EV}+P+D$

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

For Company B, from the table:
- Total EV manufactured = 120
- Percentage of petrol vehicles = 40% of $T_B$
- Percentage of diesel vehicles = 25% of petrol vehicles ($P_B$)

Therefore, we can write:
$P_B=40\%\times T_B=0.4T_B$

The number of diesel vehicles is:
$D_B=25\%\times P_B=0.25\times 0.4T_B=0.1T_B$

Now, using the total vehicle equation:
$T_B={\text{EV}}_B+P_B+D_B$

$T_B=120+0.4T_B+0.1T_B$

$T_B=120+0.5T_B$

$0.5T_B=120$

$T_B=240$

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, from the table:
- Total EV manufactured = 300
- Percentage of petrol vehicles = 25% of $T_D$
- Percentage of diesel vehicles = 60% of petrol vehicles ($P_D$)

Therefore, we can write:
$P_D=25\%\times T_D=0.25T_D$

The number of diesel vehicles is:
$D_D=60\%\times P_D=0.6\times 0.25T_D=0.15T_D$

Now, using the total vehicle equation:
$T_D={\text{EV}}_D+P_D+D_D$

$T_D=300+0.25T_D+0.15T_D$

$T_D=300+0.4T_D$

$0.6T_D=300$

$T_D=500$

Now, we find the number of diesel vehicles manufactured by D:
$D_D=0.15\times 500=75$

Step 3: Find the difference

The difference between the total vehicles manufactured by B and the diesel vehicles manufactured by D is:
$\text{Difference}=240-75=165$