Study the following information carefully and answer the given questions :
The number of cricket players in four different academies A, B, C and Dis 120, 150, 100 and 200 respectively.
There are only three types of players in a team: specialist Batsman, specialist bowlers and all-rounders (those who can both bat and ball)
Out of total number of players in academies A, B, C and D, percentage of players who can bat is `75%, 80%, 60% `and `35%` respectively.
Out of total number of players in academies A, B, C and D, percentage of players who can bowl is `50%, 60%, 70%` and `80%` respectively
Fees paid to one specialist batsman for one match is 3times the fees paid to one all-rounder for one match
Fees paid to one specialist bowler for one match is Rs20000.
Respective ratio between the fees paid to one specialist bowler for one match and the fees paid to one all-rounder for one match is 2:3.
Total fees paid to all the all-rounders of academy D is what per cent of total fees paid to all the specialist batsmen of academy A?

Options

A. `18 2/3`
B. `17 1/3`
C. `16 2/3`
D. `22 1/3`

Answer

To solve the problem step by step, we will break down the information given and calculate the required values systematically.

### Step 1: Calculate the number of batsmen in each academy.

1. **Academy A**:
- Total players = 120
- Percentage of batsmen = 75%
- Number of batsmen = \( 75\% \text{ of } 120 = \frac{75}{100} \times 120 = 90 \)

2. **Academy B**:
- Total players = 150
- Percentage of batsmen = 80%
- Number of batsmen = \( 80\% \text{ of } 150 = \frac{80}{100} \times 150 = 120 \)

3. **Academy C**:
- Total players = 100
- Percentage of batsmen = 60%
- Number of batsmen = \( 60\% \text{ of } 100 = \frac{60}{100} \times 100 = 60 \)

4. **Academy D**:
- Total players = 200
- Percentage of batsmen = 35%
- Number of batsmen = \( 35\% \text{ of } 200 = \frac{35}{100} \times 200 = 70 \)

### Step 2: Calculate the number of bowlers in each academy.

1. **Academy A**:
- Percentage of bowlers = 50%
- Number of bowlers = \( 50\% \text{ of } 120 = \frac{50}{100} \times 120 = 60 \)

2. **Academy B**:
- Percentage of bowlers = 60%
- Number of bowlers = \( 60\% \text{ of } 150 = \frac{60}{100} \times 150 = 90 \)

3. **Academy C**:
- Percentage of bowlers = 70%
- Number of bowlers = \( 70\% \text{ of } 100 = \frac{70}{100} \times 100 = 70 \)

4. **Academy D**:
- Percentage of bowlers = 80%
- Number of bowlers = \( 80\% \text{ of } 200 = \frac{80}{100} \times 200 = 160 \)

### Step 3: Calculate the number of all-rounders in each academy.

- **Academy A**:
- Total players = 120
- Batsmen + Bowlers = 90 + 60 = 150
- All-rounders = \( 150 - 120 = 30 \)

- **Academy B**:
- Total players = 150
- Batsmen + Bowlers = 120 + 90 = 210
- All-rounders = \( 210 - 150 = 60 \)

- **Academy C**:
- Total players = 100
- Batsmen + Bowlers = 60 + 70 = 130
- All-rounders = \( 130 - 100 = 30 \)

- **Academy D**:
- Total players = 200
- Batsmen + Bowlers = 70 + 160 = 230
- All-rounders = \( 230 - 200 = 30 \)

### Step 4: Calculate the fees for each type of player.

1. **Fees for Bowlers**:
- Given that the fees for one specialist bowler = Rs 20,000.
- The ratio of fees for bowlers to all-rounders is 2:3.
- Therefore, fees for one all-rounder = \( \frac{3}{2} \times 20,000 = 30,000 \).

2. **Fees for Batsmen**:
- Fees for one batsman = 3 times the fees for one all-rounder = \( 3 \times 30,000 = 90,000 \).

### Step 5: Calculate total fees for all-rounders in Academy D.

- Number of all-rounders in Academy D = 30.
- Total fees for all-rounders in Academy D = \( 30 \times 30,000 = 900,000 \).

### Step 6: Calculate total fees for specialist batsmen in Academy A.

- Number of specialist batsmen in Academy A = \( 90 - 30 = 60 \).
- Total fees for specialist batsmen in Academy A = \( 60 \times 90,000 = 5,400,000 \).

### Step 7: Calculate the percentage.

- Total fees paid to all all-rounders of Academy D as a percentage of total fees paid to all specialist batsmen of Academy A:
\[ \text{Percentage} = \left( \frac{900,000}{5,400,000} \right) \times 100 = \frac{900}{5400} \times 100 = \frac{1}{6} \times 100 = 16.67\% \]

### Final Answer:
The total fees paid to all the all-rounders of academy D is **16.67%** of total fees paid to all specialist batsmen of academy A.