Question

The weight of a bucket is 15 kg when filled with water upto 3/5 of its capacity and the weight is 19 kg if filled with water upto 4/5 it's capacityFind weight of bucket if it is completely filled with water

Answer 1

Answer:

Given,

for \dfrac{3}{4}43 capacity, weight of the bucket = 15 kg

for \dfrac{4}{5}54 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, 19 kg + 4kg = 23 kg.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+ \dfrac{3}{5}y = 15 \rightarrow  ...(1)x+53y=15→ ...(1) [according to the first condition]

x+ \dfrac{4}{5}y = 19 \rightarrow ...eq(2)x+54y=19→...eq(2) [according to the second condition]

Now let us subtract eq(2) from

eq(1) we get,

x+ \dfrac{4}{5}y = 19x+54y=19

x+ \dfrac{3}{5}y = 15x+53y=15

____________

\dfrac{4}{5}y - \dfrac{3}{5}y = 19-1554y−53y=19−15

y [\dfrac{4-3}{5}] = 4y[54−3]=4

y \times \dfrac{1}{5} = 4y×51=4

\Rightarrow y = 20⇒y=20

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

x+ \dfrac{3}{5} (20) = 15x+53(20)=15

x+12 = 15 \Rightarrow x = 15-12 \Rightarrow  x = 3.x+12=15⇒x=15−12⇒ x=3.