The sum of Rs. 530 is divided among A, B and C such that A gets Rs 70 more than B and B gets Rs. 80 more than C. Then what are their share?

Options

A. `240, 190, 100`
B. `250, 180, 100`
C. `250, 100, 180`
D. `300, 80, 100`

Answer

To solve the problem step by step, we will define the shares of A, B, and C based on the conditions given in the question.

### Step 1: Define the variables
Let:
- The share of C be \( C \)
- The share of B be \( B \)
- The share of A be \( A \)

### Step 2: Write the equations based on the problem statement
From the problem, we have the following relationships:
1. The total amount shared among A, B, and C is Rs. 530:
\[ A + B + C = 530 \quad \text{(Equation 1)} \]
2. A gets Rs. 70 more than B:
\[ A = B + 70 \quad \text{(Equation 2)} \]
3. B gets Rs. 80 more than C:
\[ B = C + 80 \quad \text{(Equation 3)} \]

### Step 3: Substitute Equation 3 into Equation 1
From Equation 3, we can express C in terms of B:
\[ C = B - 80 \]
Now substitute this expression for C into Equation 1:
\[ A + B + (B - 80) = 530 \]
This simplifies to:
\[ A + 2B - 80 = 530 \]
Now, we can rearrange this to:
\[ A + 2B = 610 \quad \text{(Equation 4)} \]

### Step 4: Substitute Equation 2 into Equation 4
Now, substitute Equation 2 into Equation 4:
\[ (B + 70) + 2B = 610 \]
This simplifies to:
\[ 3B + 70 = 610 \]
Now, subtract 70 from both sides:
\[ 3B = 540 \]
Now divide by 3:
\[ B = 180 \]

### Step 5: Find the values of A and C
Now that we have B, we can find A and C using Equations 2 and 3.

Using Equation 2:
\[ A = B + 70 = 180 + 70 = 250 \]

Using Equation 3:
\[ C = B - 80 = 180 - 80 = 100 \]

### Step 6: Final shares
Thus, the shares of A, B, and C are:
- A = Rs. 250
- B = Rs. 180
- C = Rs. 100

### Summary
The shares are:
- A: Rs. 250
- B: Rs. 180
- C: Rs. 100

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