Comprehension

Five years ago Maxam Glass Co. had estimated its staff requirements in the ve levels in their organization as: Level - 1: 55; Level - 2: 65; Level - 3: 225 ; Level - 4: 255 & Level - 5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex policemen. The following graph shows actual staff strength at various levels as on date. 

Question: 1

The level in which the Ex-Defence Servicemen are highest in percentage terms is:

Show Hint

Whenever asked for “highest in percentage terms,” always divide the subgroup (Ex-Defence Servicemen) by the total of that level, not the overall total. Then compare across all levels.
Updated On: Aug 23, 2025
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The Correct Option is D

Solution and Explanation

We need to calculate the percentage of Ex-Defence Servicemen at each organizational level. The formula is: \[ \text{Percentage} = \frac{\text{Ex-Defence Servicemen at that level}}{\text{Total Employees at that level}} \times 100 \] Step 1: Level 1 Total Employees = 52, Ex-Defence Servicemen = 6
\[ \frac{6}{52} \times 100 = 11.54% \]

Step 2: Level 2 Total Employees = 65, Ex-Defence Servicemen = 8
\[ \frac{8}{65} \times 100 = 12.31% \]

Step 3: Level 3 Total Employees = 210, Ex-Defence Servicemen = 30
\[ \frac{30}{210} \times 100 = 14.28% \]

Step 4: Level 4 Total Employees = 130, Ex-Defence Servicemen = 25
\[ \frac{25}{130} \times 100 = 19.23% \]

Step 5: Level 5 Total Employees = 330, Ex-Defence Servicemen = 60
\[ \frac{60}{330} \times 100 = 18.18% \]

Step 6: Comparison
\[ \text{Level 1: } 11.54%, \quad \text{Level 2: } 12.31%, \quad \text{Level 3: } 14.28%, \quad \text{Level 4: } 19.23%, \quad \text{Level 5: } 18.18% \] Clearly, the maximum percentage is at

Level 4 = 19.23%. \[ \boxed{\text{Level 4 has the highest percentage of Ex-Defence Servicemen.}} \]
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Question: 2

If the company decides to abolish all vacant posts at all levels, which level would incur the highest reduction in percentage terms?

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In data interpretation problems, always check whether the question demands absolute values or percentage terms. A higher number of vacancies does not always mean the highest percentage vacancy.
Updated On: Aug 23, 2025
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The Correct Option is D

Solution and Explanation

Step 1: Interpret the question.
The question asks which level will see the \emph{highest percentage reduction} if all vacant posts are abolished. This means we need to compare the ratio of vacant posts to the total sanctioned posts at each level.

Step 2: Use the given data.
From the explanation provided, the actual staff strength is 130, while the sanctioned requirement is 255. This means there are: \[ 255 - 130 = 125 \quad \text{vacant posts.} \] Among all levels, Level 4 alone has almost \emph{half of its posts vacant}.

Step 3: Compare levels.
When vacant posts are expressed as a percentage of the total strength at each level: - Levels 1, 2, 3, and 5 have fewer vacant seats relative to their sanctioned numbers.
- Level 4, however, has nearly 50% vacancy, which is far higher than any other level.

Step 4: Conclusion.
Thus, abolishing posts in Level 4 results in the \emph{highest percentage reduction}. \[ \boxed{4} \]
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Question: 3

Among all levels, which level has the lowest representation of Ex-policemen?

Show Hint

When asked for "lowest representation," always compute the percentages rather than comparing absolute values. A smaller absolute number may not always imply a smaller proportion.
Updated On: Aug 23, 2025
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The Correct Option is C

Solution and Explanation

Step 1: Calculate percentage representation at each level.
The formula is: \[ \text{Percentage representation} = \frac{\text{Ex-policemen at level}}{\text{Total staff at level}} \times 100 \] - Level 1: \(\dfrac{4}{52} \times 100 = 7.69%\)
- Level 2: \(\dfrac{4}{65} \times 100 = 6.15%\)
- Level 3: \(\dfrac{9}{210} \times 100 = 4.29%\)
- Level 4: \(\dfrac{7}{130} \times 100 = 5.38%\)
- Level 5: \(\dfrac{15}{330} \times 100 = 4.54%\)

Step 2: Compare the percentages.
- Level 1: 7.69%
- Level 2: 6.15%
- Level 3: 4.29%
- Level 4: 5.38%
- Level 5: 4.54%

Step 3: Identify the lowest.
Level 3 has the lowest representation at 4.29%. \[ \boxed{3} \]
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