Four friends A, B, C and D have some money among them one day they decided to equate the money, so first A gave B what B had initially, then B gave C what C had initially. Again C gave D what D had initially and finally D gave A what A had now . Thus each of them had equal sum of ₹ 48.
What was the initial amount of B?

Options

A. ₹ 36
B. ₹ 54
C. ₹ 45
D. ₹ 42

Answer

To solve the problem, we need to analyze the transactions that occurred among the four friends A, B, C, and D, and how these transactions led to each of them having ₹48 at the end.

### Step-by-Step Solution:

1. **Let the initial amounts be defined**:
- Let A's initial amount = A
- Let B's initial amount = B
- Let C's initial amount = C
- Let D's initial amount = D

2. **First Transaction**:
- A gives B what B had initially.
- After this transaction:
- A's amount = A - B
- B's amount = B + B = 2B

3. **Second Transaction**:
- B gives C what C had initially.
- After this transaction:
- B's amount = 2B - C
- C's amount = C + C = 2C

4. **Third Transaction**:
- C gives D what D had initially.
- After this transaction:
- C's amount = 2C - D
- D's amount = D + D = 2D

5. **Fourth Transaction**:
- D gives A what A has now (after the first transaction).
- After this transaction:
- D's amount = 2D - (A - B)
- A's amount = (A - B) + (A - B) = 2(A - B)

6. **Final Amounts**:
- After all transactions, each friend has ₹48:
- A's final amount = 2(A - B) = 48
- B's final amount = 2B - C = 48
- C's final amount = 2C - D = 48
- D's final amount = 2D - (A - B) = 48

7. **Solving for A**:
- From A's equation:
\[ 2(A - B) = 48 \implies A - B = 24 \implies A = B + 24 \]

8. **Solving for C**:
- From B's equation:
\[ 2B - C = 48 \implies C = 2B - 48 \]

9. **Solving for D**:
- From C's equation:
\[ 2C - D = 48 \implies D = 2C - 48 \]

10. **Substituting C into D's equation**:
- Substitute \(C = 2B - 48\) into \(D\):
\[ D = 2(2B - 48) - 48 = 4B - 96 - 48 = 4B - 144 \]

11. **Substituting D into B's equation**:
- Substitute \(D = 4B - 144\) into \(D's\) equation:
\[ 2D - (A - B) = 48 \implies 2(4B - 144) - (B + 24 - B) = 48 \]
\[ 8B - 288 - 24 = 48 \implies 8B - 312 = 48 \implies 8B = 360 \implies B = 45 \]

### Conclusion:
The initial amount of B was ₹45.