A 600 mL solution with 5% salt is mixed with a 300 mL solution with 8% sugar. What are the concentrations of salt and sugar in the mixture?
(i) Salt: 5%, Sugar: 8% (ii) Salt: 13%, Sugar: 3% (iii) Salt: 6%, Sugar: 6%
(iv) Salt: 5.55%, Sugar: 8.88% (v) Salt: 3.33%, Sugar: 2.67% (vi) Salt: 4.1%, Sugar: 7.08%
Step-by-step solution
To find: Concentrations of salt and of sugar in the 900 mL mixture
Idea: Each substance is in only one solution. The other solution has 0% of it, so it dilutes it. Concentration = amount of the substance ÷ total volume.
- Salt = 5% of 600 mL = 30 mL; sugar = 8% of 300 mL = 24 mL. Total volume = 600 + 300 = 900 mL.1 mark
- Salt: 30900 × 100 ≈ 3.33%; sugar: 24900 × 100 ≈ 2.67%. This is option (v).1 mark
Check: Both must be lower than before mixing, since each is diluted: 3.33 < 5 and 2.67 < 8 ✓. Options (i)–(iv) keep or raise at least one concentration, so they are impossible; (vi) lowers both, but not enough: 30 mL of salt in 900 mL is 3.33%, not 4.1%.
Answer to write in the exam
Salt = 5100 × 600 = 30 mL; sugar = 8100 × 300 = 24 mL
Total volume = 600 + 300 = 900 mL
Salt % = 30900 × 100 = 3.33%; Sugar % = 24900 × 100 = 2.67%
∴ Option (v): Salt 3.33%, Sugar 2.67%
Common mistakes that cost marks
- Thinking the concentrations stay 5% and 8% (option (i)). Mixing adds water that has none of that substance.
- Taking the weighted mean 600 × 5 + 300 × 8900 = 6% for both (option (iii)), as if salt and sugar were one substance.
- Dividing by 600 for salt and 300 for sugar instead of by the full 900 mL.
How this can come in the exam
200 mL of a 9% salt solution is mixed with 100 mL of pure water. The salt concentration becomes
- 9%
- 4.5%
- 6%
- 3%
Show answer
(C) 6%
Salt = 18 mL in 300 mL: 18300 × 100 = 6%.
Try one yourself
400 mL of a solution with 10% sugar is mixed with 100 mL of a solution with 20% salt. Find the concentrations of sugar and salt in the mixture.
Show answer
Sugar = 40 mL, salt = 20 mL in 500 mL: sugar 8%, salt 4%.
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