A vessel, full of water, weighs 24 kg. When the same vessel is 1/4 full of water, it weighs 9 kg. Find the weight (in kg) of the empty vessel (the vessel without any water).

Introduction / Context:
This problem tests forming and solving linear equations using weight compositions. The total weight of a vessel with water equals the weight of the empty vessel plus the weight of the water inside it. When the vessel is only 1/4 full, the water weight becomes 1/4 of the full-water weight, but the vessel weight remains unchanged. By writing two equations (full and quarter-full) and subtracting, you can eliminate the vessel weight and solve for the water weight, then get the empty vessel weight.

Given Data / Assumptions:

• Weight when full = 24 kg
• Weight when 1/4 full = 9 kg
• Let empty vessel weight = E kg
• Let full water weight = W kg

Concept / Approach:
Set equations: Full: E + W = 24 Quarter-full: E + (W/4) = 9 Subtract second from first to isolate W, then compute E = 24 - W.

Step-by-Step Solution:
Equation (1): E + W = 24 Equation (2): E + W/4 = 9 Subtract (2) from (1): W - W/4 = 24 - 9 (3/4)W = 15 W = 15 * (4/3) = 20 E = 24 - 20 = 4

Verification / Alternative check:
If empty vessel is 4 kg and full water is 20 kg, then at 1/4 full the water weighs 5 kg. Total becomes 4 + 5 = 9 kg, matching the given condition, so the result is consistent.

Why Other Options Are Wrong:
3 kg would imply full water weight 21 kg and quarter-full total 3 + 5.25 = 8.25, not 9. 5 kg would imply full water weight 19 and quarter-full total 5 + 4.75 = 9.75, not 9. 6 kg or 8 kg similarly fail one of the two conditions when checked.

Common Pitfalls:
Assuming 1/4 full means total weight is 1/4 of 24 (incorrect), forgetting that vessel weight is constant, or not handling the subtraction step correctly.

Final Answer:
The empty vessel weighs 4 kg.