Question

2 containers,x and y of the same capacity , are each 4/5 full of water . if 4 litres of water from container x is added to container y , the ratio of the water in the two containers becomes 2:3. What is the capacity of container x ?​

Answer 1

the answer should be 3/4

Answer 2

Given:

Two containers $x$ and $y$ with $\frac{4}{5}$ full of water and same capacities.

4 litres from container $x$ added to container $y$.

Ratio of water in the 2 containers after adding = 2:3

To find:

Capacity of container $x$.

Solution:

Let capacity of container $x$ be A and capacity of container $y$ be B.

A = B   (given)

Amount of water in $x=y=\frac{4A}{5}$  litres

On adding 4litres from $x$ to y,

Amount of water in $x=\frac{4A}{5}-4$

Amount of water in $y=\frac{4A}{5}+4$

Ratio of water in the two containers,

$\frac{2}{3}=\frac{\frac{4A}{5}-4 }{\frac{4A}{5}+4 }$

Cross-multiplying,

$2(\frac{4A}{5}+4)=3(\frac{4A}{5}-4)$

$2(\frac{4A+20}{5})=3(\frac{4A-20}{5})$

Cancelling 5 on both sides,

$2(4A+20)=3(4A-20)$

$8A+40=12A-60$

$60+40=12A-8A$

$100=4A$

$A=\frac{100}{4}=25$ litres

Container $x$ has a capacity of 25 litres.

The capacity of container $x$ is 25 litres.