In the last financial year a car company sold 41,800 cars, and in the current year its target is to sell 51,300 cars. By what percentage must the sales be increased to reach the new target?

Introduction / Context:
This question tests the concept of percentage increase, which is widely used for sales targets, company growth, and population changes. The idea is to compare the new target with the previous year's achievement and compute how much increase is required as a percentage of the original value, not of the new value.

Given Data / Assumptions:
- Last year's car sales = 41,800 cars.
- This year's target sales = 51,300 cars.
- We need the percentage increase needed relative to 41,800.
- The formula for percentage increase is (Increase / Original) * 100 percent.

Concept / Approach:
The key concept is to first compute the absolute increase in the number of cars and then express that increase as a percentage of the original sales. We must be careful to divide by the original value (last year's sales), because percentage change is always measured relative to the starting point. Once we get a decimal, we can convert it into a mixed fraction to match the given options.

Step-by-Step Solution:
Step 1: Calculate the increase in number of cars: Increase = 51,300 - 41,800.Step 2: Increase = 9,500 cars.Step 3: Use the percentage increase formula: Percentage increase = (Increase / Original) * 100.Step 4: Substitute values: Percentage increase = (9,500 / 41,800) * 100.Step 5: Compute the fraction 9,500 / 41,800, which simplifies to 95 / 418.Step 6: Now 95 / 418 * 100 is approximately 22.727 percent.Step 7: 22.727 percent corresponds to 22 8/11 percent when written as a mixed fraction.

Verification / Alternative check:
To check quickly, convert 22 8/11 percent to a decimal. Since 8/11 is approximately 0.727, 22 8/11 percent is about 22.727 percent. Multiply 41,800 by 22.727 percent (0.22727) to see if the increase is roughly 9,500 cars. 41,800 * 0.22727 is close to 9,500, which confirms that the percentage is consistent with the target.

Why Other Options Are Wrong:
- 11 9/22 percent and 8 9/22 percent: These values are too small and do not produce an increase of 9,500 cars when applied to 41,800.
- 8 11/23 percent: This is also too low and does not match the calculated fraction 95 / 418.

Common Pitfalls:
One frequent mistake is to divide the increase by the new target instead of by the original value, which would underestimate the required growth. Another is rounding too early, which can slightly change the fraction and make it hard to match the provided options. Always compute the increase first, then divide by the original base value, and only then convert the result carefully into a fraction or mixed number.

Final Answer:
The sales must be increased by 22 8/11 percent to reach the new target.