Question

How many kg of pure salt must be added to 30 kg of 2% solution of salt and water to increase it to a 10% solution?

Answer 1

- Hint: We can find pure salt amount by writing a given statement in terms of equation. We can write an equation that the amount of pure salt and amount of salt in solution of 30 kg will be equal to 10% of total solution amount.

Complete step-by-step solution -
As given there is 2% salt in 30 kg solution of salt and water.
So amount of salt in 30 kg solution is
$\Rightarrow 30\,kg\times \dfrac{2}{100}$
$\Rightarrow 0.6kg$
The amount of pure salt added is x kg.
So total amount of salt is $(0.6+x)kg$
When x kg of pure salt added then total amount of solution is $(30+x)kg$
Now according to the question $(0.6+x)kg$ is 10% of $(30+x)kg$.
So we can write it as
$\Rightarrow (0.6+x)=\dfrac{10}{100}\times (30+x)$
$\Rightarrow 0.6+x=0.1(30+x)$
$\Rightarrow 0.6+x=3+0.1x$
$\Rightarrow x-0.1x=3-0.6$
$\Rightarrow 0.9x=2.4$
$\Rightarrow x=\dfrac{2.4}{0.9}$
$\Rightarrow x=2.667kg$
So we need to add 2.667kg of pure salt in 30 kg of 2% solution of salt and water to increase it to a 10% solution.

Note: We need to remember that when we add some amount of pure salt in solution then the total amount of solution will be increased. That’s why we add 30kg and x kg to get a total amount of solution.