Question

How many liters of a 10% salt solution should be added to 80 liters of a 35% salt solution to obtain a mixture that is 30% salt solution?

Answer 1

Solution:

Let x litres of 10% salt solution,

$\sf \implies \: 30 \% = \frac{x \: of \: 10\% + 80 \: of \: 35\%}{x + 80} \\ \\ \implies \sf \: \: \frac{30}{100} = \frac{x \times \frac{10}{100} + 80 \times \frac{35}{100} }{x + 80} \\ \\ \\ \\ \sf \implies \: 10x \: + 2800 = 30(x + 80) \\ \\ \sf \implies \: 10x + 2800 = 30x + 2400 \\ \\ \sf \implies \:30x - 10x = 2800 - 2400 \\ \\ \sf \implies 20x = 400 \\ \\ \sf \implies \: x = \frac{400}{20} \\ \\ \implies \sf \: x = 20\%$