If `13/15` of an estate be worth Rs. `390`, then `3/5` of it is-

Options

A. Rs. 320
B. Rs. 270
C. Rs. 450
D. Rs. 324

Answer

To solve the problem step by step, we start by defining the variables and using the information given in the question.

### Step 1: Define the variable
Let the total value of the estate be represented by \( X \).

### Step 2: Set up the equation
According to the problem, \( \frac{13}{15} \) of the estate is worth Rs. 390. Therefore, we can write the equation:
\[ \frac{13}{15} X = 390 \]

### Step 3: Solve for \( X \)
To find \( X \), we need to isolate it. We can do this by multiplying both sides of the equation by \( \frac{15}{13} \):
\[ X = 390 \times \frac{15}{13} \]

### Step 4: Calculate \( X \)
Now, we perform the multiplication:
\[ X = 390 \times \frac{15}{13} = 390 \times 15 \div 13 \]
Calculating \( 390 \times 15 \):
\[ 390 \times 15 = 5850 \]
Now, divide by 13:
\[ X = \frac{5850}{13} = 450 \]

### Step 5: Find \( \frac{3}{5} \) of \( X \)
Now that we have \( X = 450 \), we need to find \( \frac{3}{5} \) of it:
\[ \frac{3}{5} X = \frac{3}{5} \times 450 \]

### Step 6: Calculate \( \frac{3}{5} X \)
Calculating \( \frac{3}{5} \times 450 \):
\[ \frac{3 \times 450}{5} = \frac{1350}{5} = 270 \]

### Final Answer
Thus, \( \frac{3}{5} \) of the estate is Rs. 270.