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.
What is the total fees paid to 3 all-rounders A1, A2 and A3 who played six, seven and eight matches respectively? (in Rs lakh)

Options

A. 6.3
B. 4.8
C. 7.2
D. 5.1

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the Fees for All-Rounders
1. **Given Information**:
- Fees paid to one specialist bowler for one match = Rs 20,000.
- The ratio of fees paid to one specialist bowler and one all-rounder = 2:3.

2. **Calculating the Fees for All-Rounders**:
- Let the fees for one all-rounder be \( x \).
- From the ratio, we have:
\[ \frac{20000}{x} = \frac{2}{3} \]
- Cross-multiplying gives:
\[ 2x = 60000 \implies x = 30000 \]
- Therefore, the fees paid to one all-rounder for one match = Rs 30,000.

### Step 2: Calculate Total Fees for All-Rounders A1, A2, and A3
1. **Matches Played**:
- A1 played 6 matches.
- A2 played 7 matches.
- A3 played 8 matches.

2. **Calculating Total Fees**:
- Total fees for A1:
\[ \text{Fees for A1} = 6 \times 30000 = 180000 \]
- Total fees for A2:
\[ \text{Fees for A2} = 7 \times 30000 = 210000 \]
- Total fees for A3:
\[ \text{Fees for A3} = 8 \times 30000 = 240000 \]

3. **Calculating Overall Total Fees**:
- Total fees for all three all-rounders:
\[ \text{Total Fees} = 180000 + 210000 + 240000 = 630000 \]

### Step 3: Convert Total Fees to Lakhs
- Since 1 lakh = 100,000, we convert the total fees:
\[ \text{Total Fees in Lakhs} = \frac{630000}{100000} = 6.3 \text{ lakh} \]

### Final Answer
The total fees paid to all-rounders A1, A2, and A3 who played 6, 7, and 8 matches respectively is **6.3 lakh**.

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