Solving the Bank E Technical and Finance Officer Ratio Problem

This question asks us to determine how many additional Technical Officers (TOs) are needed in Bank E to achieve a specific ratio with Finance Executives (FEs), given the total vacant posts in Bank E and the percentage breakup of different cadres across all banks.

Analysing the Given Data Tables

We are provided with two tables:

We need to focus on Bank E and the cadres of Technical Officers (TO) and Finance Executives (FE).

Calculating Required Officers in Bank E

From Table 1, the total number of vacant posts in Bank E is 450. From Table 2, the percentage requirement for TOs is 8%, and for FEs is 26%. We assume these percentages apply to the total vacant posts in Bank E.

• Required number of TOs in Bank E: $8\%$ of $450 = \frac{8}{100} \times 450 = 0.08 \times 450 = 36$
• Required number of FEs in Bank E: $26\%$ of $450 = \frac{26}{100} \times 450 = 0.26 \times 450 = 117$

So, currently, Bank E requires 36 TOs and 117 FEs based on the standard percentage breakup.

Setting Up the Target Ratio and Equation

The question asks how many more TOs should be employed so that the ratio of TOs to FEs becomes $2:3$. Let 'x' be the number of additional TOs to be employed.

• New number of TOs = (Required TOs) + (Additional TOs) = $36 + x$
• Number of FEs remains = $117$

The target ratio of the new number of TOs to the number of FEs is $2:3$. We can write this as an equation:

$$ \frac{\text{New number of TOs}}{\text{Number of FEs}} = \frac{2}{3} $$

Substituting the values:

$$ \frac{36 + x}{117} = \frac{2}{3} $$

Solving for the Additional TOs (x)

Now, we solve the equation for 'x':

• Cross-multiply: $3 \times (36 + x) = 2 \times 117$
• Distribute the 3: $108 + 3x = 234$
• Subtract 108 from both sides: $3x = 234 - 108$
• Calculate the difference: $3x = 126$
• Divide by 3 to find x: $x = \frac{126}{3}$
• Calculate the value of x: $x = 42$

Therefore, 42 more TOs should be employed in Bank E so that the ratio of the number of TOs to that of number of FEs becomes $2:3$. The new number of TOs would be $36 + 42 = 78$. The ratio would then be $78 : 117$. Dividing both by 39 (which is a common factor, $39 \times 2 = 78$ and $39 \times 3 = 117$) gives $2:3$, which matches the target ratio.

Summary of Calculation Steps

1. Identify total vacant posts in Bank E (450).
2. Calculate the initial required number of TOs (8% of 450 = 36).
3. Calculate the required number of FEs (26% of 450 = 117).
4. Set up the equation based on the target ratio of TOs to FEs as 2:3, including 'x' for additional TOs.
5. Solve the equation $\frac{36 + x}{117} = \frac{2}{3}$ for x.
6. The value of x is the number of additional TOs needed.

The number of additional TOs required is 42.

Revision Table: Bank E Officer Calculation

Additional Information: Data Interpretation Tips

Data interpretation questions often require extracting specific information from tables or charts and performing calculations based on that data. Here are some tips:

• Read the question carefully to understand exactly what is being asked.
• Identify the relevant data sources (which table, which row/column).
• Pay attention to units and percentages.
• Break down complex problems into smaller steps.
• Set up equations clearly when ratios or unknown quantities are involved.
• Double-check calculations, especially when dealing with percentages and ratios.
• Ensure the final answer addresses the specific question asked (e.g., "how many more", not just the final number).
• Practice with different types of data representation (tables, bar graphs, pie charts, line graphs).

Understanding percentages and ratios is crucial for solving many data interpretation problems like this one involving Bank E and the TO/FE ratio.