Question

Read the information given carefully and answer the question that follows: 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 electri(c); State 2 had 20% of the total cars in the ratio of 5:3:2 (diesel, petrol and electri(c); State 3 had 30% of the total cars in the ratio of 4:5:3 (diesel, petrol and electri(c), and; State 4 had 35% of the total cars in the ratio of 7:5:2 (diesel, petrol and electri(c). What is the ratio of diesel cars in State 4 to electric cars in State 3?

• A. 3:7
• B. 5:7
• C. 7:3
• D. 7:4
• E. 4:7

Hint:

Calculate each state's total cars first, then distribute according to the given ratios.

Answer 1

The Correct Option is C

Step 1: Total cars = 8000. State 1: 15% = $0.15 \times 8000 = 1200$ cars. Ratio 3:4:1 → sum = 8. Diesel = $\frac{3}{8} \times 1200 = 450$, Petrol = $\frac{4}{8} \times 1200 = 600$, Electric = $\frac{1}{8} \times 1200 = 150$.
Step 2: State 2: 20% = $0.20 \times 8000 = 1600$ cars. Ratio 5:3:2 → sum = 10. Diesel = $\frac{5}{10} \times 1600 = 800$, Petrol = $\frac{3}{10} \times 1600 = 480$, Electric = $\frac{2}{10} \times 1600 = 320$.
Step 3: State 3: 30% = $0.30 \times 8000 = 2400$ cars. Ratio 4:5:3 → sum = 12. Diesel = $\frac{4}{12} \times 2400 = 800$, Petrol = $\frac{5}{12} \times 2400 = 1000$, Electric = $\frac{3}{12} \times 2400 = 600$.
Step 4: State 4: 35% = $0.35 \times 8000 = 2800$ cars. Ratio 7:5:2 → sum = 14. Diesel = $\frac{7}{14} \times 2800 = 1400$, Petrol = $\frac{5}{14} \times 2800 = 1000$, Electric = $\frac{2}{14} \times 2800 = 400$.
Step 5: Ratio of diesel in State 4 to electric in State 3 = $1400 : 600 = 14 : 6 = 7 : 3$.
Step 6: Final Answer: 7:3.