Question

300 g of sugar solution has 40% of sugar in it. How much sugar should be added to make it 50% in the solution?

• A. 40g
• B. 60g
• C. 80g
• D. 120g

Answer 1

Answer:

B. 60g

Understanding Mixture Problems

• Mixture problems, especially those involving percentages, are a very common topic in competitive exams. They test your ability to work with proportions and algebraic equations.

• The key to solving such problems is to identify the constant component. In this case, when sugar is added, the amount of water remains unchanged.

Step-by-step Calculation:

1. Initial Solution Breakdown:

   • The total sugar solution is 300 g.

   • It contains 40% sugar.

   • Amount of sugar initially = 40% of 300 g = (40/100) * 300 = 120 g.

   • Amount of water initially = Total solution - Amount of sugar = 300 g - 120 g = 180 g.

2. Desired Final State:

   • We want the new solution to have 50% sugar.

   • Since only sugar is added, the amount of water remains constant at 180 g.

   • If the new solution has 50% sugar, it implies that the remaining 50% must be water.

3. Calculating New Total Solution:

   • If 180 g of water represents 50% of the new solution, then the total new solution (100%) can be found by doubling the water amount.

   • New total solution = 180 g / 0.50 = 360 g (or 180 g * 2 = 360 g).

4. Determining Sugar to be Added:

   • The new total amount of sugar required in the 360 g solution is 50% of 360 g = (50/100) * 360 = 180 g.

   • Amount of sugar already present = 120 g.

   • Sugar to be added = New sugar amount - Initial sugar amount = 180 g - 120 g = 60 g.