Question

The weight of a bucket is $15kg$. When it is filled water upto $\frac{3}{5}$ of its capacity in weight is $19kg$. If it is filled with water up to $\frac{4}{5}th$ of its capacity. Find the weight of the empty bucket if it is completely filled with water.

Answer 1

REF.Image

Given,

for $\frac{3}{4}$ capacity, weight of the bucket = 15 kg

for $\frac{4}{5}$ capacity, weight of the bucket = 19 kg

Let us consider each division of bucket

is of 4 units capacity. So according

for fig (b) we get 15 kg + 4 kg = 19 kg.

Similarly, Let us find out the weight

of a completely filled bucket

we, get, $19kg+4kg=23kg.$ [fig (d)]

Now,

Let us assume,

weight of an Empty bucket = y kg

weight of completely filled bucket = x kg

Now,

as per the given conditions is the question we get,

$x+\frac{3}{5}y=15\to ...\left(1\right)$ [according to the first condition]

$x+\frac{4}{5}y=19\to ...eq\left(2\right)$ [according to the second condition]

Now let us subtract eq(2) from

eq(1) we get,

$x+\frac{4}{5}y=19$

$x+\frac{3}{5}y=15$

____________

$\frac{4}{5}y-\frac{3}{5}y=19-15$

$y\left[\frac{4-3}{5}\right]=4$

$y\times \frac{1}{5}=4$

$\Rightarrow y=20$

Let us now substitute 'y' in eq (1) we get,

$x+\frac{3}{5}\left(20\right)=15$

$x+12=15\Rightarrow x=15-12\Rightarrow x=3.$

$\therefore$ weight of an empty bucket $\Rightarrow y=20kg$

along with capacity of some rational amount.

and rest space the amount of weight that to be filled

$\Rightarrow x=3kg.$

Now,

$\therefore x+y=3+20=23kg$

$\therefore$ The weight of the bucket when it is filled

completely = 23 kg