A solution of 100 litres has a 60% salt concentration. How many litres of water must be added to reduce the concentration to 40%, and then how much pure salt must be added to bring the concentration back to 50%?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. Add 50 L of water, then 30 L of salt.
Initial solution = 100 L
Salt = 60 L and Water = 40 L
To make 40% salt: Let water added = x L
60/(100 + x) = 40/100 = 0.4
⇒ 60 = 40 + 0.4x
⇒ 0.4x = 20
⇒ x = 50 L of water added
Now mixture = 100 + 50 = 150 L, 60 L salt, 90 L water.
To make 50% salt: Let salt added = y L.
(60 + y)/(150 + y) = 1/2 = 0.5
⇒ 60 + y = 75 + 0.5y
⇒ 0.5y = 15
⇒ y = 30 L salt added