Question

A vessel full of water weighs 16.5 kg. When the vessel is half full, it weighs 10.5 kg. Find the weight of the empty vessel

Answer 1

Let the weight (mass) of the vessels be x kilograms and let the weight of the water be y kilograms. 

Mass of the vessels full of the water = 16.5 kg.
∴ x + y = 16.5 
⇒ x = 16.5 - y -------eq(i)

Also, the mass of the vessel when half water is present in its = 10.5 kg. 
∴ x + y/2 = 10.5 
∴ 16.5 - y + 0.5y = 10.5
⇒ 16.5 - 0.5y = 10.5 
∴  0.5y = 16.5 - 10.5
⇒ 0.5y = 6
∴ y/2 = 6
∴ y = 12 kg. 

Thus, the weight of the water in the vessel = 12 kg.

∴ x = 16.5 - 12
    = 4.5 kg.

Hence, the weight of the empty vessels is 4.5 kg.


Hope it helps.

Answer 2

Here, we are considering two masses, one of the vessel and the other of the water inside it.

Let us consider the weight of the vessel to be 'x',
and that of the water inside it to be 'y'.

From the first sentence, we can infer that
x + y = 16.5

The next sentence mentions that the vessel is half full. As the weight of the vessel cannot change, it is obvious that half of the water in the vessel has been emptied. Thus,

x + $\frac{y}{2}$ = 10.5

By solving these two simultaneous equations, we can find out the answer. Let us subtract the second equation from the first. Thus,

     x + y = 16.5
-  (x  + $\frac{y}{2}$ = 10.5 )
---------------------------------------------------
y - $\frac{y}{2}$ = 6

 $\frac{y}{2}$ = 6

y = 6*2
y = 12 kg

Thus, the weight of the water in the vessel is 12 kg. Hence, the weight of the vessel will be 16.5 - 12 = 4.5

Therefore, the weight of the empty vessel is 4.5 kg.