A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?

The correct option is 10 kg.

Step-by-step Explanation:

Step 1: Define the variables
Let the weight of the empty vessel be $V$ kg.
Let the weight of the water when the vessel is completely full be $W$ kg.

Step 2: Formulate the equations from the given information
1. A vessel full of water weighs 40 kg:

$V+W=40$

$V+\frac{1}{3}W=20$

Step 3: Solve the system of equations
Subtract the second equation from the first equation to eliminate $V$:

$(V+W)-(V+\frac{1}{3}W)=40-20$

$W-\frac{1}{3}W=20$

$\frac{2}{3}W=20$

$W=20\times \frac{3}{2}=30\text{ kg}$

Step 4: Find the weight of the empty vessel
Substitute $W=30$ back into the first equation:

$V+30=40$

$V=40-30=10\text{ kg}$

Therefore, the weight of the empty vessel is 10 kg.