Question

Pehal and Ishaan were making 100g sugar solutions with concentration by mass 20% and 50% respectively. Pehal added 20g of sugar in her solution whereas Ishaan evaporated 20g of water from his solution. Now, the two solutions were mixed to form a final solution.The concentration by mass of final solution is
(1) 28%
(2) 45%
(3) 40%
(4) 60%

Answer 1

45%is the concentration

Answer 2

Answer : The concentration by mass of final solution is 45%

Explanation :

20% solution will contain 20 grams of sugar in 100 grams of solution.

Mass of water used to make this solution would be 100 - 20 = 80 g

Pehal makes her 100 g of 20% solution by dissolving 20 g sugar in 80 g water.

She adds additional 20 grams of sugar in her solution.

Therefore Pehal's solution now contains 40 g sugar in 80 g water.

Ishaan makes his 50% solution by dissolving 50 g sugar in 100 g solution.

Mass of water used by him is 100 -50 = 50g.

Ishaan prepares his 50% solution by dissolving 50 g sugar in 50 g water.

Ishaan then evaporates 20 g of water from his solution.

Therefore his new solution would contain 50 g sugar in 30 g water.

After mixing the solutions, we get

total mass of sugar = 40 g + 50 g = 90 g

total mass of water = 80 g + 30 g = 110 g

total mass of solution = 90 g + 110 g = 200 g.

Concentration of new solution = $\frac{90g}{200g} \times 100 = 45%$

The concentration by mass of final solution is 45%