Multiple choice

Pehal and Ishaan were making $100g$ sugar solution 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 solutions were mixed to form a final solution, The concentration by mass of final solution is:

  1. $28\%$
  2. $45\%$
  3. $40\%$
  4. $60\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Pehal's solution initially contains 20 g of sugar and 80 g of water, then she adds 20 g of sugar, giving 40 g sugar in 120 g solution. Ishaan's solution contains 50 g sugar, and evaporating 20 g water leaves 50 g sugar in 80 g solution. The mixture has 90 g sugar in 200 g total solution, so its concentration is 45%.

AI explanation

Initially, Pehal has 20g of sugar in 100g solution, and adding 20g of sugar makes her new mass 120g with 40g of sugar, yielding a 33.33% concentration. Ishaan starts with 50g of sugar in 100g solution, and evaporating 20g of water leaves 80g of solution with 50g of sugar, yielding a 62.5% concentration. By the method of alligation, the differences between the new concentrations and the final desired concentration must be equal, giving 62.5 minus x and x minus 33.33, but we can simply sum the total sugar (40g plus 50g = 90g) and total mixture mass (120g plus 80g = 200g). The final concentration by mass is 90 divided by 200, which is 45%.

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