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A chemist has 20 liters of a solution that is 30% salt. How many liters of pure water must be added to dilute the solution to 20% salt?

A chemist has 20 liters of a solution that is 30% salt. How many liters of pure water must be added to dilute the solution to 20% salt?

Answer and explanation

Answer: A: 10

Adding pure water changes the volume but not the amount of salt. The original solution has 0.30×20=60.30 \times 20 = 6 liters of salt. After adding ww liters of water, the volume is 20+w20 + w and the salt is 20% of it: 0.20(20+w)=60.20(20 + w) = 6. So 20+w=3020 + w = 30 and w=10w = 10, choice A. Check: 630=20%\frac{6}{30} = 20\%. Choice B (6) is the amount of salt, not water. Choice C (15) would give 35 liters at about 17%. Choice D (20) would double the volume and dilute the solution to 15%. Track the salt, which stays constant.

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