Correct Option
10kg
Let V represent the weight of the empty vessel and W represent the weight of the water when the vessel is completely full.
From the problem statement, two linear equations can be established:
- The vessel full of water weighs 40 kg: V + W = 40 kg (Equation 1)
- The vessel one-third filled with water weighs 20 kg: V + (1/3)W = 20 kg (Equation 2)
To determine the weight of the water (W), subtract Equation 2 from Equation 1:
(V + W) - (V + (1/3)W) = 40 - 20
W - (1/3)W = 20
(2/3)W = 20
W = (20 * 3) / 2
W = 30 kg
Now, substitute the calculated value of W (30 kg) into Equation 1 to find the weight of the empty vessel (V):
V + 30 = 40
V = 40 - 30
V = 10 kg
Therefore, the weight of the empty vessel is 10 kg.
Incorrect Options
Options 2, 3, and 4 are incorrect as they do not satisfy the conditions presented in the problem statement when substituted as the weight of the empty vessel.
- If the empty vessel weighed 15 kg (Option 2), the total water capacity would be 40 - 15 = 25 kg. A one-third filled vessel would then weigh 15 + (1/3)*25 = 23.33 kg, which contradicts the given weight of 20 kg.
- If the empty vessel weighed 20 kg (Option 3), the total water capacity would be 40 - 20 = 20 kg. A one-third filled vessel would then weigh 20 + (1/3)*20 = 26.67 kg, which contradicts the given weight of 20 kg. This option represents the weight of the vessel when one-third filled, not the empty vessel.
- If the empty vessel weighed 25 kg (Option 4), the total water capacity would be 40 - 25 = 15 kg. A one-third filled vessel would then weigh 25 + (1/3)*15 = 30 kg, which contradicts the given weight of 20 kg.
Only an empty vessel weight of 10 kg is consistent with both conditions provided in the problem.