A vessel full of water weight 40kg if it is half filled it's weight is 30kg find the weight of empty vessel
Let's call the weight of the empty vessel "x" kg.
According to the given information, when the vessel is completely full, it weighs 40 kg.
When the vessel is half-filled, it weighs 30 kg.
This means that the weight of the water in the vessel is 40 kg - x kg = 10 kg.
Since the vessel is half-filled, the weight of the water is half of the weight when it is completely full, which means it is 10 kg.
So, 10 kg is the weight of the water in the vessel, which means that the weight of the empty vessel (x kg) is 30 kg - 10 kg = 20 kg.
Therefore, the weight of the empty vessel is 20 kg.
Let's assume the weight of the empty vessel is represented by "x" kg.
Based on the information given, we know that when the vessel is full, it weighs 40 kg.
When the vessel is half-filled, it weighs 30 kg.
This means that the weight of the water alone is 40 kg - 30 kg = 10 kg.
Since the vessel is half-filled with water, we can conclude that the weight of the empty vessel is equal to the weight of the full vessel minus the weight of the water alone.
Thus, the weight of the empty vessel is 40 kg - 10 kg = 30 kg.
Therefore, the weight of the empty vessel is 30 kg.
To find the weight of the empty vessel, we need to find the weight of the water in the vessel when it is fully filled.
We are given that when the vessel is fully filled, its weight is 40kg. When it is half filled, its weight is 30kg.
Let's assume the weight of the water in the vessel when it is fully filled is 'w' kg.
According to the given information, the weight of the water plus the weight of the empty vessel is 40 kg when the vessel is full. So, we can write the equation:
w + weight of empty vessel = 40 kg
Similarly, when the vessel is half filled, the weight of the water plus the weight of the empty vessel is 30 kg. So, we can write another equation:
0.5w + weight of empty vessel = 30 kg
Now we have a system of two equations:
w + weight of empty vessel = 40 kg ---(1)
0.5w + weight of empty vessel = 30 kg ---(2)
To solve this system of equations, we can subtract equation (2) from equation (1) to eliminate the weight of the empty vessel:
(w + weight of empty vessel) - (0.5w + weight of empty vessel) = 40 kg - 30 kg
Simplifying this equation, we get:
w - 0.5w = 10 kg
0.5w = 10 kg
Dividing both sides of the equation by 0.5, we find:
w = 20 kg
So, the weight of the water in the vessel when it is fully filled is 20 kg.
Now, to find the weight of the empty vessel, we substitute the value of 'w' into either equation (1) or (2):
w + weight of empty vessel = 40 kg
20 kg + weight of empty vessel = 40 kg
Subtracting 20 kg from both sides of the equation, we find:
weight of empty vessel = 40 kg - 20 kg
weight of empty vessel = 20 kg
Therefore, the weight of the empty vessel is 20 kg.