A solution of sugar is obtained by mixing 200 g of its 25 solution and 500 g of its 40 solution (both by mass). The mass percentage of the resulting sugar solution is (Nearest integer)

Given: - Solution (I): mass of solution = 200 g, sugar percentage = 25 - Solution (II): mass of solution = 500 g, sugar percentage = 40 Find: The mass percentage of sugar in the resulting mixed solution. Mass of sugar in solution (I): 25100 200 = 50 g Mass of sugar in solution (II): 40100 500 = 200 g Total mass of solution: 200 + 500 = 700 g Total mass of sugar: 50 + 200 = 250 g Now, the final percentage of sugar is: 250700 100 = 35.71 36 Therefore, the mass percentage of the resulting sugar solution is 36. The correct option is B.

A solution of sugar is obtained by mixing 200 g of its 25 solutio… — Solution | JEE Chemistry

MCQEasyJEE 2023Concentration Terms (Molarity, Molality, etc.)

A solution of sugar is obtained by mixing $200 \, \text{g}$ of its $25\%$ solution and $500 \, \text{g}$ of its $40\%$ solution (both by mass). The mass percentage of the resulting sugar solution is _____ (Nearest integer)

A
$35$
B
$36$
C
$37$
D
$38$

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given:

Solution (I): mass of solution = $200 \, \text{g}$ , sugar percentage = $25\%$
Solution (II): mass of solution = $500 \, \text{g}$ , sugar percentage = $40\%$

Find: The mass percentage of sugar in the resulting mixed solution.

Mass of sugar in solution (I):

\frac{25}{100} \times 200 = 50 \, \text{g}

Mass of sugar in solution (II):

\frac{40}{100} \times 500 = 200 \, \text{g}

Total mass of solution:

200 + 500 = 700 \, \text{g}

Total mass of sugar:

50 + 200 = 250 \, \text{g}

Now, the final percentage of sugar is:

\frac{250}{700} \times 100 = 35.71 \approx 36

Therefore, the mass percentage of the resulting sugar solution is $36\%$ . The correct option is B.

Common mistakes

Using $25\%$ and $40\%$ directly to average the percentages is incorrect because the two solutions have different masses. First find the actual mass of sugar in each solution, then divide by the total mass.
Treating $200 \, \text{g}$ and $500 \, \text{g}$ as masses of sugar is wrong. They are masses of the solutions, so the sugar mass must be calculated using the given percentages.
Forgetting to use the total mass of the mixed solution, $700 \, \text{g}$ , in the denominator gives an incorrect percentage. Always divide total solute mass by total solution mass.

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Answer

Step-by-step solution

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