Automobiles are the most preferred mode of transport because they allow us to cover large distance quickly. Resultantly, vehicles have been developed that run on diesel, petrol and even on electricity, which is a remarkable innovative development. During a survey about the percentage wise distribution of cars in four different states, the information regarding ratio between the diesel engine cars, petrol engine cars and electric cars was collected. Total number of cars for which data was collected was 8000. Of these, State 1 had 15% of the total cars in the ratio of 3:4:1 (diesel, petrol and electric); State 2 had 20% of the total cars in the ratio of 5:3:2 (diesel, petrol and electric); State 3 had 30% of the total cars in the ratio of 4:5:3 (diesel, petrol and electric), and; State 4 had 35% of the total cars in the ratio of 7:5:2 (diesel, petrol and electric).

What is the average number of diesel cars in all the States?

The correct option is 862.5.

Step-by-Step Explanation:

First, let us note the total number of cars surveyed across all states:

$\text{Total number of cars}=8000$

We are given the percentage distribution of total cars in each state and the ratio of diesel, petrol, and electric cars in each state. Let us calculate the number of diesel engine cars state by state.

1. Diesel cars in State 1:

State 1 has 15% of the total cars. The ratio of (diesel : petrol : electric) is 3 : 4 : 1.

Sum of ratio terms for State 1 = 3 + 4 + 1 = 8.

Total cars in State 1:

$\text{Total cars (State 1)}=15\%\text{ of }8000=\frac{15}{100}\times 8000=1200$

Number of diesel cars in State 1:

$\text{Diesel cars (State 1)}=\frac{3}{8}\times 1200=3\times 150=450$

2. Diesel cars in State 2:

State 2 has 20% of the total cars. The ratio of (diesel : petrol : electric) is 5 : 3 : 2.

Sum of ratio terms for State 2 = 5 + 3 + 2 = 10.

Total cars in State 2:

$\text{Total cars (State 2)}=20\%\text{ of }8000=\frac{20}{100}\times 8000=1600$

Number of diesel cars in State 2:

$\text{Diesel cars (State 2)}=\frac{5}{10}\times 1600=800$

3. Diesel cars in State 3:

State 3 has 30% of the total cars. The ratio of (diesel : petrol : electric) is 4 : 5 : 3.

Sum of ratio terms for State 3 = 4 + 5 + 3 = 12.

Total cars in State 3:

$\text{Total cars (State 3)}=30\%\text{ of }8000=\frac{30}{100}\times 8000=2400$

Number of diesel cars in State 3:

$\text{Diesel cars (State 3)}=\frac{4}{12}\times 2400=\frac{1}{3}\times 2400=800$

4. Diesel cars in State 4:

State 4 has 35% of the total cars. The ratio of (diesel : petrol : electric) is 7 : 5 : 2.

Sum of ratio terms for State 4 = 7 + 5 + 2 = 14.

Total cars in State 4:

$\text{Total cars (State 4)}=35\%\text{ of }8000=\frac{35}{100}\times 8000=2800$

Number of diesel cars in State 4:

$\text{Diesel cars (State 4)}=\frac{7}{14}\times 2800=\frac{1}{2}\times 2800=1400$

5. Total Diesel Cars across all 4 States:

$\text{Total Diesel Cars}=450+800+800+1400=3450$

6. Average Number of Diesel Cars per State:

$\text{Average}=\frac{\text{Total Diesel Cars}}{\text{Number of States}}=\frac{3450}{4}=862.5$

Hence, the average number of diesel cars in all the States is 862.5.