Question

Container A has 300 grams of salt water with 13% concentration. Container B has 700 grams of salt water with 7% concentration. After we take out a certain amount of solution from Container A and the same amount from container B, we pour what we take out from A into B and vice versa. Now the two containers have the same concentration. How many grams of solution did we take out from each container?

Answer 1

210 grams

Explanation:

Simply, the final amount of each container will not be changed because we add and subtract same amount of solution in the end. Therefore final mass of Container A is 300 grams and final mass of Container B is 700 grams.

However if concentration of the both containers is the same, final amont of the salt should have following relation;

`(m_(A))/(m_B)=(3)/(7)`

where
`m_A` is the amount of salt in container A, and
`m_B` is the amount of salt in container B.

Suppose that the x is the amount that we take away from both containers and than pour into other container. For container A, finally we will have (300-x) grams with 13% concentration and x grams with 7% concentration and vice versa. Total amount of salt in container can be written as,

`m_A=(300-x)*(13)/(100) +x*(7)/(100)=(3900-6x)/(100)`

similarly for container B ,

`m_B=(700-x)*(7)/(100) +x*(13)/(100)=(4900+6x)/(100)`

if we replace these values in first equation above and solve for the x,

`(m_A)/(m_B)=(3900-6x)/(4900+6x)=(3)/(7)`

`7*3900- 42x=3*4900+18x\\60x=12600\\x=210`