Two glasses of equal quantities of lemonade are prepared. One glass has 10% jaggery and the other has 20% jaggery. If we mix the lemonade from both glasses, what is the concentration of jaggery in the mixture?
Answer: The mixture has 15% jaggery, midway between 10% and 20%, because the two glasses hold equal quantities.
Step-by-step solution
Given: Two glasses with equal quantities of lemonade, say y each; Jaggery: 10% in one glass, 20% in the other
To find: Concentration of jaggery in the mixture
To find: Concentration of jaggery in the mixture
Idea: Concentration = quantity of jaggery in the mixturequantity of the mixture. Find the jaggery from each glass, add, and divide by the total lemonade.
- Let each glass hold y of lemonade. Jaggery in the glasses: 10100y = 0.1y and 20100y = 0.2y.½ mark
- Concentration = quantity of jaggery in the mixturequantity of the mixture = 0.1y + 0.2yy + y = 0.3y2y.1 mark
- = 0.15 = 15%. With equal quantities, the mixture is exactly midway between 10% and 20%.½ mark
The concentration of jaggery in the mixture is 15%.
Check: Try y = 200 mL: jaggery = 20 + 40 = 60 mL in 400 mL, and 60400 = 0.15 = 15% ✓.
Answer to write in the exam
Let quantity of lemonade in each glass = y
Concentration = 0.1y + 0.2yy + y
= 0.3y2y = 0.15
∴ Concentration of jaggery in the mixture = 15%
Common mistakes that cost marks
- Adding the percentages: 10% + 20% = 30%. Concentrations are averaged (weighted by quantity), never added.
- Dividing by y instead of 2y; the mixture has twice the lemonade of one glass.
- Writing 0.15 as 0.15% instead of 15%.
How this can come in the exam
MCQ (1 mark)
Equal volumes of milk with 4% fat and 6% fat are mixed. The fat content of the mixture is
- 5%
- 10%
- 4.8%
- 2.4%
Show answer
(A) 5%
Equal quantities, so the concentration is midway: 4 + 62 = 5%.
Try one yourself
Equal quantities of syrup with 8% sugar and 14% sugar are mixed. Find the concentration of sugar in the mixture.
Show answer
0.08y + 0.14y2y = 0.11 = 11%.
More questions like this
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