Ankit invested twice than that of Ayush , while Charu invested thrice than that of Ankit and ratio between time period in investment of Ayush , Ankit & Charu is `6 : 3 : 8` . If difference between profit share of Charu and Ayush is Rs 7980 , then find total profit of all three together .

Options

A. A)11400 Rs
B. B)11800 Rs
C. C)11600 Rs
D. D)11200 Rs

Answer

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

### Step 1: Define Investments
Let Ayush's investment be represented as \( A \).
- According to the problem, Ankit invested twice as much as Ayush:
\[ \text{Ankit's investment} = 2A \]
- Charu invested thrice as much as Ankit:
\[ \text{Charu's investment} = 3 \times (2A) = 6A \]

### Step 2: Define Time Periods
The time periods for Ayush, Ankit, and Charu are given in the ratio \( 6:3:8 \).
- Let the time period for Ayush be \( 6x \),
- For Ankit, it will be \( 3x \),
- For Charu, it will be \( 8x \).

### Step 3: Calculate Profit Shares
The profit share for each person can be calculated using the formula:
\[ \text{Profit Share} = \text{Investment} \times \text{Time} \]
- For Ayush:
\[ \text{Profit Share of Ayush} = A \times (6x) = 6Ax \]
- For Ankit:
\[ \text{Profit Share of Ankit} = (2A) \times (3x) = 6Ax \]
- For Charu:
\[ \text{Profit Share of Charu} = (6A) \times (8x) = 48Ax \]

### Step 4: Establish Profit Ratio
Now we can establish the profit ratio:
\[ \text{Profit Ratio} = \text{Ayush} : \text{Ankit} : \text{Charu} = 6Ax : 6Ax : 48Ax = 1 : 1 : 8 \]

### Step 5: Use Given Profit Difference
We know that the difference between Charu's and Ayush's profit share is Rs 7980:
\[ \text{Difference} = \text{Charu's Profit} - \text{Ayush's Profit} = 48Ax - 6Ax = 42Ax \]
Setting this equal to 7980:
\[ 42Ax = 7980 \]
To find \( Ax \):
\[ Ax = \frac{7980}{42} = 190 \]

### Step 6: Calculate Total Profit
Now we can find the total profit:
\[ \text{Total Profit} = \text{Ayush's Profit} + \text{Ankit's Profit} + \text{Charu's Profit} \]
Using the profit ratio:
\[ \text{Total Profit} = 6Ax + 6Ax + 48Ax = 60Ax \]
Substituting \( Ax = 190 \):
\[ \text{Total Profit} = 60 \times 190 = 11400 \]

### Final Answer
Thus, the total profit of all three together is Rs 11400.

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