Calculating Bank Staff Retrenchment Percentage Difference

The problem asks us to find the percentage difference in retrenchment of Probationary Officers (POs) between Bank D and Bank F. We are given the total number of vacant posts in each bank and the percentage breakup of required personnel across different cadres, including POs.

According to Table 2, the percentage breakup for Probationary Officers (PO) cadre is 10% for any bank. This means that 10% of the total vacant posts in a bank are for POs.

Step 1: Calculate the required number of POs for Bank D and Bank F

From Table 1:

• Vacant posts in Bank D = 820
• Vacant posts in Bank F = 560

Required POs in Bank D:

\(\text{Required POs in D} = \text{Vacant Posts in D} \times \text{PO Percentage}\)

\(\text{Required POs in D} = 820 \times 10\% = 820 \times \frac{10}{100} = 82\)

Required POs in Bank F:

\(\text{Required POs in F} = \text{Vacant Posts in F} \times \text{PO Percentage}\)

\(\text{Required POs in F} = 560 \times 10\% = 560 \times \frac{10}{100} = 56\)

Step 2: Calculate the number of POs hired by Bank D and Bank F

The problem states that Banks D and F hired 15% more POs than their requirement.

POs hired by Bank D:

\(\text{POs hired by D} = \text{Required POs in D} \times (1 + \text{Extra Percentage})\)

\(\text{POs hired by D} = 82 \times (1 + 15\%) = 82 \times (1 + \frac{15}{100}) = 82 \times 1.15 = 94.3\)

POs hired by Bank F:

\(\text{POs hired by F} = \text{Required POs in F} \times (1 + \text{Extra Percentage})\)

\(\text{POs hired by F} = 56 \times (1 + 15\%) = 56 \times (1 + \frac{15}{100}) = 56 \times 1.15 = 64.4\)

Step 3: Calculate the number of retrenchments in Bank D and Bank F

After one year, the staff strength was brought down to the original requirement. The number of retrenchments is the difference between the number of POs hired and the original requirement.

Retrenchment in Bank D:

\(\text{Retrenchment in D} = \text{POs hired by D} - \text{Required POs in D}\)

\(\text{Retrenchment in D} = 94.3 - 82 = 12.3\)

Retrenchment in Bank F:

\(\text{Retrenchment in F} = \text{POs hired by F} - \text{Required POs in F}\)

\(\text{Retrenchment in F} = 64.4 - 56 = 8.4\)

Step 4: Calculate the percentage difference in retrenchment between Bank D and Bank F

We need to find by what percent the retrenchment in Bank D is less/more than in Bank F. This means we calculate the percentage difference relative to Bank F's retrenchment.

\(\text{Percentage Difference} = \frac{\text{Retrenchment in D} - \text{Retrenchment in F}}{\text{Retrenchment in F}} \times 100\)

\(\text{Percentage Difference} = \frac{12.3 - 8.4}{8.4} \times 100\)

\(\text{Percentage Difference} = \frac{3.9}{8.4} \times 100\)

\(\text{Percentage Difference} \approx 0.4642857 \times 100 \approx 46.43\%\)

Since the retrenchment in Bank D (12.3) is greater than the retrenchment in Bank F (8.4), the retrenchment in Bank D is 46.43% more than in Bank F.

Summary of Calculations

Comparison:

\(\frac{\text{Retrenchment in D} - \text{Retrenchment in F}}{\text{Retrenchment in F}} \times 100 = \frac{12.3 - 8.4}{8.4} \times 100 \approx 46.43\%\)

Retrenchment in D is more than in F.

Therefore, the retrenchment is approximately 46.43% more in Bank D than in Bank F.

Revision Table: Key Concepts in Bank Staffing Calculations

Additional Information: Data Interpretation in Banking Exams

Data Interpretation (DI) questions, like this one involving bank vacant posts and cadre breakups, are common in banking and other competitive exams. They test your ability to read, analyze, and interpret data presented in tables, charts, or graphs to answer specific questions.

• Understanding Tables: Carefully read the titles, row headers, and column headers to understand what data is presented in each table.
• Extracting Relevant Data: Identify the specific numbers needed for the calculation based on the question. In this case, it was vacant posts for Banks D and F, and the PO percentage.
• Performing Calculations: Apply the given conditions (like hiring 15% more) and standard mathematical operations (percentage calculation, subtraction, percentage difference) accurately.
• Attention to Detail: Pay close attention to keywords like "more than requirement" and "brought down to original strength," which dictate the calculation steps. Also, note whether the percentage difference is asked relative to Bank D or Bank F, and whether it's 'more' or 'less'.
• Using Percentages: Remember how to calculate a percentage of a number (\(\frac{\text{Percentage}}{100} \times \text{Number}\)) and how to calculate a percentage increase or decrease.

Mastering these skills is crucial for efficiently solving DI problems and scoring well in competitive examinations.