A and B have together three times what B and Chave, while A, B, C together have thirty rupees more than that of A. If B has 5 times that of C, then A has

Options

A. Rs 60
B. RS 65
C. Rs75
D. Rs 45

Answer

To solve the problem step by step, we will define variables for the amounts of money that A, B, and C have. Let's denote:

- A = amount of money A has
- B = amount of money B has
- C = amount of money C has

### Step 1: Set up the equations based on the problem statement

1. According to the first condition, A and B together have three times what B and C have:
\[ A + B = 3(B + C) \]

2. The second condition states that A, B, and C together have thirty rupees more than A:
\[ A + B + C = A + 30 \]

3. The third condition tells us that B has five times what C has:
\[ B = 5C \]

### Step 2: Simplify the equations

From the first equation:
\[ A + B = 3B + 3C \]
Rearranging gives:
\[ A = 3B + 3C - B \]
\[ A = 2B + 3C \]

From the second equation:
\[ A + B + C = A + 30 \]
Subtracting A from both sides gives:
\[ B + C = 30 \]

### Step 3: Substitute B in terms of C

Using the third equation \(B = 5C\), we can substitute B in the equation \(B + C = 30\):
\[ 5C + C = 30 \]
\[ 6C = 30 \]
Dividing both sides by 6 gives:
\[ C = 5 \]

### Step 4: Find B using C

Now that we have C, we can find B:
\[ B = 5C = 5 \times 5 = 25 \]

### Step 5: Find A using B and C

Now we can substitute B and C back into the equation for A:
\[ A = 2B + 3C \]
Substituting the values of B and C:
\[ A = 2(25) + 3(5) \]
Calculating gives:
\[ A = 50 + 15 = 65 \]

### Final Answer

Thus, A has **65 rupees**.

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