Question

Pehal and Ishaan were making 100 g sugar solutions with concentration by mass 20% and 50% respectively. Pehal added 20 g of sugar in her solution whereas Ishaan evaporated 20 g 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

Answer:- 45%

Solution:- Original concentration of the sugar solution made by pehal is 20% by mass. It means 20 grams of sugar in 100 g of solution.

Mass of water in Pehal's solution = 100 g - 20 g = 80 g

Similarly, original sugar solution made by Ishaan is 50% by mass means 50 g of sugar in 100 g of solution.

mass of water in Ishaan's solution = 100 g - 50 g = 50 g

pehal added 20 g of sugar in her original solution. So, total sugar in the solution = 20 g + 20 g = 40 g

Ishaan evaporated 20 g of water from his solution. So, new amount of water in his solution = 50 g - 20 g = 30 g

Now, the two solutions are added. So, total mass of sugar in the final solution = 40 g + 50 g = 90 g

Total mass of water in final solution = 80 g + 30 g = 110 g

Mass of final solution = 90 g + 110 g = 200 g

Concentration by mass of final solution =  

$(\frac{sugar}{solution})*100$

= $(\frac{90}{200})*100$

= 45%

Hence, the concentration by mass of final sugar solution is 45%.