Alligation–Mixture (Weighing a Vessel):\nA vessel full of water weighs 24 kg. When the vessel is 1/4 full, it weighs 9 kg. Find the weight of the empty vessel (kg).

Introduction / Context:
This is a linear equation problem treating vessel and water weights separately.

Given Data / Assumptions:

• Full: vessel + water = 24 kg.
• Quarter-full: vessel + 1/4 water = 9 kg.
• Water density taken as 1 kg/L (proportionality across fill levels).

Concept / Approach:
Let empty vessel weigh V and full water weigh W. Then V + W = 24 and V + (1/4)W = 9. Solve for V.

Step-by-Step Solution:
1) Subtract equations: (V+W) − (V+W/4) = 24 − 9 ⇒ (3/4)W = 15.2) W = 15 * (4/3) = 20.3) V = 24 − W = 24 − 20 = 4 kg.

Verification / Alternative check:
Quarter-full weight = 4 + 20/4 = 9 kg (checks).

Why Other Options Are Wrong:
5, 8, 3 kg violate one or both equations.

Common Pitfalls:
Mistaking quarter-full as subtracting 1/4 of total weight 24 directly (incorrect).

Final Answer:
4 kg