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.
In a team of 11 players, having 4 specialist batsmen, 4 specialist bowlers and 3 all-rounders, what is the total fees paid to the whole team together ? (in Rs lakh)

Options

A. 7.1
B. 6.7
C. 5.3
D. 3.9

Answer

To solve the problem, we will break it down step by step.

### Step 1: Determine the Fees for Each Type of Player
1. **Specialist Bowler's Fee**: Given as Rs. 20,000.
2. **All-Rounder's Fee**: The ratio of the fees paid to one specialist bowler and one all-rounder is 2:3. Therefore, if the bowler's fee is Rs. 20,000 (which corresponds to 2 parts), we can find the all-rounder's fee (3 parts):
\[ \text{All-Rounder's Fee} = \frac{3}{2} \times 20,000 = 30,000 \]
3. **Specialist Batsman's Fee**: It is given that the fee for one specialist batsman is three times that of one all-rounder:
\[ \text{Batsman's Fee} = 3 \times 30,000 = 90,000 \]

### Step 2: Calculate Total Fees for the Team
The team consists of:
- 4 Specialist Batsmen
- 4 Specialist Bowlers
- 3 All-Rounders

Now, we will calculate the total fees for each type of player.

1. **Total Fees for Batsmen**:
\[ \text{Total Fees for Batsmen} = 4 \times 90,000 = 360,000 \]

2. **Total Fees for Bowlers**:
\[ \text{Total Fees for Bowlers} = 4 \times 20,000 = 80,000 \]

3. **Total Fees for All-Rounders**:
\[ \text{Total Fees for All-Rounders} = 3 \times 30,000 = 90,000 \]

### Step 3: Calculate the Overall Total Fees
Now, we will add up all the fees:
\[ \text{Total Fees} = \text{Total Fees for Batsmen} + \text{Total Fees for Bowlers} + \text{Total Fees for All-Rounders} \]
\[ \text{Total Fees} = 360,000 + 80,000 + 90,000 = 530,000 \]

### Step 4: Convert to Lakhs
Since the question asks for the total fees in lakhs:
\[ \text{Total Fees in Lakhs} = \frac{530,000}{100,000} = 5.3 \text{ lakhs} \]

### Final Answer
The total fees paid to the whole team together is **5.3 lakhs**.

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