Vehicles have been developed that run on diesel, petrol and 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.
The 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).
Solution
Total cars in all the four states = 8000
Now, for State 1:
Total number of cars = 15% of the total cars = 15% of 8000 = 1200
Now, the number of diesel, petrol and electric cars are in the ratio of 3:4:1.
Total number of diesel cars = $$\dfrac{3}{3+4+1}\times1200=450$$
Total number of petrol cars = $$\dfrac{4}{3+4+1}\times1200=600$$
Total number of electric cars = $$\dfrac{1}{3+4+1}\times1200=150$$
Now, for State 2:
Total number of cars = 20% of the total cars = 20% of 8000 = 1600
Now, the number of diesel, petrol and electric cars are in the ratio of 5:3:2.
Total number of diesel cars = $$\dfrac{5}{5+3+2}\times1600=800$$
Total number of petrol cars = $$\dfrac{3}{5+3+2}\times1600=480$$
Total number of electric cars = $$\dfrac{2}{5+3+2}\times1600=320$$
Now, for State 3:
Total number of cars = 30% of the total cars = 30% of 8000 = 2400
Now, the number of diesel, petrol and electric cars are in the ratio of 4:5:3.
Total number of diesel cars = $$\dfrac{4}{4+5+3}\times2400=800$$
Total number of petrol cars = $$\dfrac{5}{4+5+3}\times2400=1000$$
Total number of electric cars = $$\dfrac{3}{4+5+3}\times2400=600$$
Now, for State 4:
Total number of cars = 35% of the total cars = 35% of 8000 = 2800
Now, the number of diesel, petrol and electric cars are in the ratio of 7:5:2.
Total number of diesel cars = $$\dfrac{7}{7+5+2}\times2800=1400$$
Total number of petrol cars = $$\dfrac{5}{7+5+2}\times2800=1000$$
Total number of electric cars = $$\dfrac{2}{7+5+2}\times2800=400$$
Hence, the distribution of the cars are as follows:
Now, Number of diesel cars in state 4 = 1400
Number of electric cars in state 3 = 600
Ratio = $$\dfrac{1400}{600}=\dfrac{7}{3}$$
Hence, the ratio of the number of diesel cars in state 4 to the number of electric cars in state 3 is 7:3.
$$\therefore\ $$ The required answer is 7:3.
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