Question

The weight of a bucket is 15kg when it is filled with water 3/5th if it’s capacity and the weight is 19kg if it is filled with water upto 4/5th of it’s capacity find the total weight of the bucket if it’s completely filled with water

Answer 1

Answer:

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Let the weight of empty bucket be x kg.

Let the weight of water the empty bucket can hold to it's full capacity be y kg.

Now,

according to the first condition,

$\\ x + \frac{3}{5}y = 15 \\ \\ 5x + 3y = 75.........(1)$

Now,

according to the second condition,

$\\ x+ \dfrac{4}{5}y = 19......(2) \\ \\ 5x + 4y = 95$

Subtracting eq.2 from eq.1

$\: \: \: \: \: 5x + 3y = 95 \\ \: \: \: \: \: 5x + 4y = 75 \\ \: ( - ) \: ( - ) \: \: ( - ) \\ - - - - - - - - - \\ \: \: \: \: \: \: \: \: \: - y \: \: \: \: = - 20$

Therefore,

y=20.

Substituting y=20 in eq.1 we get

$\\ 5x + 3(20) = 75 \\ \\ 5x + 60 = 75 \\ \\ \: \: \: \: \: \: \: \: \: \: 5x = 75 - 60 \\ \\ \: \: \: \: \: \: \: \: \: 5x = 15 \\ \\ \: \: \: \: \: \: \: \: \: \: \: x = \frac{15}{5} \\ \\ \: \: \: \: \: \: \: \: \: \: \: x = 3 \\ \\ the \: weight \: of \: water \: when \: it \: is \: completely \: filled \: with \: water \\= x + y \\ = 3 + 20 \\ = 23kg$