Correct option is C

Given:

From State B:

Formula:

$$\text{Percentage shortlisted} = \left( \frac{S}{E} \right) \times 100$$​​

​Solution:
​$$\begin{aligned}&\text{Calculate percentage for each post:} \\&\bullet \ \text{I: } \left( \frac{220}{3200} \right) \times 100 = 6.875\% \\&\bullet \ \text{II: } \left( \frac{420}{8500} \right) \times 100 = 4.94\% \\&\bullet \ \text{III: } \left( \frac{190}{8400} \right) \times 100 = 2.26\% \\&\bullet \ \text{IV: } \left( \frac{320}{6200} \right) \times 100 = 5.16\% \\&\bullet \ \text{V: } \left( \frac{180}{5800} \right) \times 100 = 3.10\% \\&\bullet \ \text{VI: } \left( \frac{430}{6200} \right) \times 100 = \mathbf{6.94\%} \\\\&\text{\textcolor{green}{\checkmark Highest is for Post VI (6.94\%)}} \\\end{aligned}$$​​
Answer: (C) VI

Correct option is D

Given:
Eligible candidates for Post III from all states:

A: 5200

B: 8400

C: 7600

D: 2600

E: 3800

F: 4400

G: 6000
​
Formula:

​$${Average} = \frac{\text{Sum of values}}{\text{Number of states}}$$​​

​Solution:
Sum = 5200 + 8400 + 7600 + 2600 + 3800 + 4400 + 6000 = 38,000
Number of states = 7

​$${Average} = \frac{38000}{7} \approx \boxed{5428.57} \\\\{Approximate Answer: } \boxed{5500}$$

Approximate average ≈ 5500

Answer: (D) 5500​​

Correct option is D

Given:

We are asked to calculate the percentage for Post I, using the values from all states.

From the table:

Formula:

$${Percentage} = \left( \frac{\text{Total Short-listed}}{\text{Total Eligible}} \right) \times 100$$​

Solution:

​$$\begin{aligned}&\text{Total Eligible (Post I)} = 2500 + 3200 + 2800 + 2400 + 3000 + 4800 + 6500 = 25200 \\&\text{Total Short-listed (Post I)} = 65 + 220 + 280 + 85 + 120 + 325 + 550 = 1645 \\\\&\text{Percentage} = \left( \frac{1645}{25200} \right) \times 100 \approx 6.527 \approx \boxed{6.5\%}\end{aligned}$$​​

Correct option is A

Given:

We are to find the ratio of total short-listed candidates from:

• State E
• State G

Step 1: Extract Short-listed (S) values

State E:

• Post I: 120
• Post II: 280
• Post III: 75
• Post IV: 280
• Post V: 260
• Post VI: 520
  Total (E) = 120 + 280 + 75 + 280 + 260 + 520 = 1535

State G:

• Post I: 550
• Post II: 140
• Post III: 325
• Post IV: 220
• Post V: 410
• Post VI: 200
  Total (G) = 550 + 140 + 325 + 220 + 410 + 200 = 1845

Step 2: Ratio

​$$\begin{aligned}&\text{Ratio (E:G)} = \frac{1535}{1845} \\\\&\text{Divide numerator and denominator by 5:} \\&\frac{1535 \div 5}{1845 \div 5} = \frac{307}{369}\end{aligned}$$

Final Answer:
307:369
​
​​

Correct option is D

Solution:

Step 1: Extract eligible candidates

Post I (Eligible - E):

• A: 2500
• B: 3200
• C: 2800
• D: 2400
• E: 3000
• F: 4800
• G: 6500

Total for Post I = 2500+3200+2800+2400+3000+4800+6500 = 25200

Post VI (Eligible - E):

• A: 5400
• B: 6200
• C: 3700
• D: 4800
• E: 7800
• F: 8800
• G: 2700

Total Eligible for Post VI = 5400 + 6200 + 3700 + 4800 + 7800 + 8800 + 2700 = 39400

​$${Percentage} = \left( \frac{25200}{39400} \right) \times 100 \approx 63.96 \approx \boxed{64\%}$$​​

Correct option is B

Given: Extract data for Post IV (Eligible and Short-listed)

Solution: Calculate percentage for each state

​$$\begin{aligned}&\text{Post IV Eligible (E) and Short-listed (S):} \\&\text{A: } \left( \frac{200}{3600} \right) \times 100 = 5.56\% \\&\text{B: } \left( \frac{320}{6200} \right) \times 100 \approx 5.16\% \\&\text{C: } \left( \frac{440}{8200} \right) \times 100 \approx 5.37\% \\&\text{D: } \left( \frac{350}{7500} \right) \times 100 \approx 4.67\% \\&\text{E: } \left( \frac{280}{6800} \right) \times 100 \approx 4.12\% \\&\text{F: } \left( \frac{180}{4700} \right) \times 100 \approx \mathbf{3.83\%} \\&\text{G: } \left( \frac{220}{5500} \right) \times 100 = 4.00\% \\\\&\text{Lowest percentage is for State } \boxed{\text{F}}\end{aligned}$$​​

Correct option is C

Given:

Post V (S):

• A: 110

• B: 180

• C: 310

• D: 160

• E: 260

• F: 220

• G: 410

Post VI (S):

• A: 380

• B: 430

• C: 250

• D: 360

• E: 520

• F: 640

• G: 200

Solution:

​$$\begin{aligned}&\text{Total Short-listed for Post V} = 110 + 180 + 310 + 160 + 260 + 220 + 410 = 1650 \\&\text{Total Short-listed for Post VI} = 380 + 430 + 250 + 360 + 520 + 640 + 200 = 2780 \\\\&\text{Ratio (Post V : Post VI)} = \frac{1650}{2780} = \boxed{165 : 278}\end{aligned}$$​​