Rs. 1,200 is divided between A, B & C such that part of A is Rs. 200 more than B's part and Rs. 200 less than C's part. B's part is

Options

A. ₹ 400
B. ₹ 600
C. ₹ 200
D. ₹ 100

Answer

To solve the problem, we need to set up equations based on the information given about the amounts received by A, B, and C.

1. **Define the Variables:**
Let B's part be represented as \( B \).
According to the problem:
- A's part is \( A = B + 200 \) (A is Rs. 200 more than B)
- C's part is \( C = A + 200 \) (C is Rs. 200 more than A)

2. **Substituting A's Value:**
We can substitute A's value into C's equation:
\[ C = (B + 200) + 200 = B + 400 \]

3. **Setting Up the Total:**
The total amount distributed among A, B, and C is Rs. 1200:
\[ A + B + C = 1200 \]
Substituting the expressions for A and C:
\[ (B + 200) + B + (B + 400) = 1200 \]

4. **Combining Like Terms:**
Combine the terms:
\[ 3B + 600 = 1200 \]

5. **Isolating B:**
Now, subtract 600 from both sides:
\[ 3B = 1200 - 600 \]
\[ 3B = 600 \]

6. **Solving for B:**
Divide both sides by 3:
\[ B = \frac{600}{3} = 200 \]

Thus, B's part is Rs. 200.