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 ratio of diesel cars in State 4 to electric cars in State 3?

The correct option is 7:3.

Let us break down the total number of cars and calculate the required numbers step-by-step.

Step 1: Total Number of Cars

Total number of cars = 8000

Step 2: Calculate the number of Diesel Cars in State 4

State 4 accounts for 35% of the total number of cars.

Total cars in State 4 =

$35\%\×8000=\frac{35}{100}\×8000=2800$

The ratio of Diesel, Petrol, and Electric cars in State 4 is 7 : 5 : 2.

Sum of ratio terms for State 4 =

$7+5+2=14$

Number of Diesel cars in State 4 =

$\frac{7}{14}\×2800=1400$

Step 3: Calculate the number of Electric Cars in State 3

State 3 accounts for 30% of the total number of cars.

Total cars in State 3 =

$30\%\×8000=\frac{30}{100}\×8000=2400$

The ratio of Diesel, Petrol, and Electric cars in State 3 is 4 : 5 : 3.

Sum of ratio terms for State 3 =

$4+5+3=12$

Number of Electric cars in State 3 =

$\frac{3}{12}\×2400=600$

Step 4: Find the required ratio

Ratio of Diesel cars in State 4 to Electric cars in State 3 =

$1400:600=7:3$

Thus, the required ratio is 7:3.