# A full of water bucket is 32 kg. When the water is half, the bucket weight is 20 kg. What was the only bucket weight?

Mar 30, 2018

The weight of bucket $= 8$ kg.

#### Explanation:

Let the weight of bucket $= x$ kg.

and the weight of water in full bucket $= w$ kg.

So the weight of water in half bucket $= \frac{w}{2}$ kg.

The full of water bucket weight $= 32$ kg.

i.e. color(red)(x+w=32..........to(1)

When the water is half the bucket weight $= 20$ kg.

i.e. $x + \frac{w}{2} = 20$

=>color(red)(2x+w=40.........to(2)

Solving $\left(2\right) \mathmr{and} \left(1\right) ,$ we get ........color(red)({(2)-(1)}

$2 x + w = 40$

$\underline{- x - w = - 32}$

$\implies x = 8$

The weight of bucket $= 8$ kg.