Divide Rs. 6940 in such a way that a ges `2/3` rd of what B gets and B gets `3/5` th of what C gets? What is the share of A and B together?

Options

A. Rs. 1982
B. Rs. 138
C. rs. 3470
D. None of these

Answer

To solve the problem of dividing Rs. 6940 among A, B, and C based on the given ratios, we can follow these steps:

### Step 1: Define the relationships
We know from the problem that:
- A gets \( \frac{2}{3} \) of what B gets.
- B gets \( \frac{3}{5} \) of what C gets.

Let’s denote:
- The amount B gets as \( B \).
- The amount C gets as \( C \).
- The amount A gets as \( A \).

From the relationships, we can express A and C in terms of B:
- \( A = \frac{2}{3}B \)
- \( B = \frac{3}{5}C \)

### Step 2: Express C in terms of B
From the equation \( B = \frac{3}{5}C \), we can rearrange it to express C in terms of B:
\[ C = \frac{5}{3}B \]

### Step 3: Write the total amount equation
The total amount distributed among A, B, and C is Rs. 6940:
\[ A + B + C = 6940 \]

Substituting the expressions for A and C in terms of B:
\[ \frac{2}{3}B + B + \frac{5}{3}B = 6940 \]

### Step 4: Combine the terms
To combine the terms, we first need a common denominator. The common denominator for the fractions is 3:
\[ \frac{2}{3}B + \frac{3}{3}B + \frac{5}{3}B = 6940 \]
\[ \frac{2B + 3B + 5B}{3} = 6940 \]
\[ \frac{10B}{3} = 6940 \]

### Step 5: Solve for B
To isolate B, multiply both sides by 3:
\[ 10B = 6940 \times 3 \]
\[ 10B = 20820 \]
Now, divide both sides by 10:
\[ B = 2082 \]

### Step 6: Calculate A and C
Now that we have B, we can find A and C:
- For A:
\[ A = \frac{2}{3}B = \frac{2}{3} \times 2082 = 1388 \]
- For C:
\[ C = \frac{5}{3}B = \frac{5}{3} \times 2082 = 3470 \]

### Step 7: Find the share of A and B together
Now, we need to find the total share of A and B:
\[ A + B = 1388 + 2082 = 3470 \]

### Final Answer
The share of A and B together is Rs. 3470.

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