A and B have together three times what B and C have, 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. Rs 75
D. Rs 45

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given in the question.

### Step 1: Define Variables
Let:
- A = amount A has
- B = amount B has
- C = amount C has

### Step 2: Set Up the First Equation
According to the problem, A and B together have three times what B and C have. This can be expressed as:
\[ A + B = 3(B + C) \]

### Step 3: Set Up the Second Equation
It is also given that A, B, and C together have thirty rupees more than A. This can be expressed as:
\[ A + B + C = A + 30 \]
From this, we can simplify to:
\[ B + C = 30 \] (Equation 1)

### Step 4: Set Up the Third Equation
We are told that B has 5 times what C has. This can be expressed as:
\[ B = 5C \] (Equation 2)

### Step 5: Substitute Equation 2 into Equation 1
Now, we can substitute Equation 2 into Equation 1:
\[ 5C + C = 30 \]
This simplifies to:
\[ 6C = 30 \]
Thus, we find:
\[ C = 5 \]

### Step 6: Find B using C
Now that we have C, we can find B using Equation 2:
\[ B = 5C = 5 \times 5 = 25 \]

### Step 7: Substitute B and C into the First Equation
Now, we can substitute the values of B and C back into the first equation to find A:
\[ A + B = 3(B + C) \]
Substituting B and C:
\[ A + 25 = 3(25 + 5) \]
\[ A + 25 = 3 \times 30 \]
\[ A + 25 = 90 \]

### Step 8: Solve for A
Now, we solve for A:
\[ A = 90 - 25 \]
\[ A = 65 \]

### Final Answer
Thus, A has **65 rupees**.

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