The average price of 3 diamonds of same weights is Rs. 5 crore, where the average price of the two costlist diamonds is double the price of the cheapest diamond.The price of the costlist diamond is :

Options

A. 5 crore
B. 6 crore
C. 8 crore
D. can't be determined

Answer

To solve the problem step by step, we will define the variables and use the information given in the question to find the price of the costliest diamond.

### Step-by-Step Solution

1. **Define Variables:**
Let the price of the costliest diamond be \( c_1 \), the price of the second costliest diamond be \( c_2 \), and the price of the cheapest diamond be \( c_3 \).

2. **Use the Average Price Information:**
The average price of the three diamonds is given as Rs. 5 crore. Therefore, we can write the equation:
\[ \frac{c_1 + c_2 + c_3}{3} = 5 \text{ crore} \]
Multiplying both sides by 3 gives:
\[ c_1 + c_2 + c_3 = 15 \text{ crore} \quad \text{(Equation 1)} \]

3. **Use the Information about Costliest Diamonds:**
The average price of the two costliest diamonds is double the price of the cheapest diamond. This can be expressed as:
\[ \frac{c_1 + c_2}{2} = 2c_3 \]
Multiplying both sides by 2 gives:
\[ c_1 + c_2 = 4c_3 \quad \text{(Equation 2)} \]

4. **Substitute Equation 2 into Equation 1:**
Now, we substitute Equation 2 into Equation 1:
\[ (c_1 + c_2) + c_3 = 15 \text{ crore} \]
Replacing \( c_1 + c_2 \) with \( 4c_3 \):
\[ 4c_3 + c_3 = 15 \text{ crore} \]
This simplifies to:
\[ 5c_3 = 15 \text{ crore} \]

5. **Solve for \( c_3 \):**
Dividing both sides by 5 gives:
\[ c_3 = 3 \text{ crore} \]

6. **Find \( c_1 + c_2 \):**
Now, using Equation 2 to find \( c_1 + c_2 \):
\[ c_1 + c_2 = 4c_3 = 4 \times 3 \text{ crore} = 12 \text{ crore} \]

7. **Conclusion:**
We have \( c_1 + c_2 = 12 \text{ crore} \), but we do not have enough information to determine the individual values of \( c_1 \) and \( c_2 \). Therefore, we cannot determine the exact price of the costliest diamond \( c_1 \).

### Final Answer:
The price of the costliest diamond cannot be determined with the given information.