A medium question on percentages and mixtures for P5–P6, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P6 first round and finals: discounts, a rise followed by a fall, and mixtures.
The question
Ming is making a dessert with 380 g of sugar water at 30%.
It tastes too sweet, so Ming wants to add plain water to bring the concentration down to 25%.
How many grams of water must Ming add?
Show the hints (2)
💡Hint 1: Before and after adding water, does the weight of sugar change?
💡Hint 2: Find the grams of sugar first. In the new solution it makes up 25%; how heavy is the new solution?
Worked solution
Have a go first, then read the solution step by step.
1.Sugar: 380 × 30 ÷ 100 = 114 g, the same before and after.
2.114 g of sugar is 25%: the new solution weighs 114 × 100 ÷ 25 = 456 g.
3.Water to add: 456 − 380 = 76 g.
⚠️Common mistake: answering 456 g. That is the whole solution after adding water; take away the 380 g there was to begin with.
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