Analyzing Software Engineer Data from the Table

The problem requires us to analyze the provided table which details the number of Assistant Software Engineers (ASE), Junior Software Engineers (JSE), and Senior Software Engineers (SSE) across five different software companies (A-E) in the year 2020. We are then asked to calculate a new percentage difference between the total number of ASEs and SSEs after specific percentage changes are applied to the original totals.

Understanding the Given Data

First, let's consolidate the relevant data from the table for ASEs and SSEs for each company:

Calculating Original Total Engineers

Next, we need to calculate the total number of ASEs and SSEs across all five companies before any changes are applied.

• Total Original ASEs = $150 + 350 + 200 + 250 + 150 = 1100$
• Total Original SSEs = $150 + 200 + 350 + 450 + 350 = 1500$

Applying Percentage Changes

The problem states that the number of ASEs employed in all five companies is increased by 20%, and the number of SSEs employed is decreased by 20%.

Let's calculate the new total numbers:

• Increase in ASEs = $20\%$ of $1100 = \frac{20}{100} \times 1100 = 0.20 \times 1100 = 220$
• New Total ASEs = Original Total ASEs + Increase in ASEs = $1100 + 220 = 1320$
• Decrease in SSEs = $20\%$ of $1500 = \frac{20}{100} \times 1500 = 0.20 \times 1500 = 300$
• New Total SSEs = Original Total SSEs - Decrease in SSEs = $1500 - 300 = 1200$

Calculating the Percentage Difference

We now have the new total number of ASEs ($1320$) and the new total number of SSEs ($1200$). The question asks for the percent by which the number of ASEs will be more than that of SSEs.

To find this percentage, we calculate the difference between the new totals and then express this difference as a percentage of the new total number of SSEs.

• Difference = New Total ASEs - New Total SSEs = $1320 - 1200 = 120$
• Percentage more than SSEs = $\left( \frac{\text{Difference}}{\text{New Total SSEs}} \right) \times 100$
• Percentage more than SSEs = $\left( \frac{120}{1200} \right) \times 100$
• Percentage more than SSEs = $\left( \frac{1}{10} \right) \times 100$
• Percentage more than SSEs = $10\%$

Therefore, after the changes, the number of ASEs will be 10% more than the number of SSEs.

Revision Table: Key Calculations

Percentage ASEs more than SSEs: $\left( \frac{1320 - 1200}{1200} \right) \times 100 = \left( \frac{120}{1200} \right) \times 100 = 10\%$

Additional Information: Percentage Calculations

Percentage calculations are fundamental in data interpretation problems. Understanding how to calculate a percentage increase or decrease, and how to find the percentage difference between two quantities, is crucial.

• Percentage Increase: If a value $V_{original}$ increases by $P\%$, the new value is $V_{new} = V_{original} \times \left(1 + \frac{P}{100}\right)$.
• Percentage Decrease: If a value $V_{original}$ decreases by $P\%$, the new value is $V_{new} = V_{original} \times \left(1 - \frac{P}{100}\right)$.
• Percentage A is more than B: $\left( \frac{A - B}{B} \right) \times 100$. This measures the difference relative to quantity B.
• Percentage A is less than B: $\left( \frac{B - A}{B} \right) \times 100$. This also measures the difference relative to quantity B.

In this problem, we calculated the new totals after a percentage change and then found the percentage by which the new total ASEs exceeded the new total SSEs, using the new total SSEs as the base for comparison.