A hard question on percentages and mixtures for 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
A dessert shop's chef has prepared a big jug of 1900 g of sugar water at 20% for sweetening.
After 1000 g has been used, the chef finds it not sweet enough and decides to add sugar to what is left in the jug to raise the concentration to 36%.
How many grams of sugar must the chef add?
Show the hints (3)
💡Hint 1: After some sugar water is used, has the concentration of what is left changed?
💡Hint 2: When sugar is added, the sugar goes up — but what stays the same?
💡Hint 3: 900 g is left, of which 720 g is water; after adding sugar, water is 64% of the solution.
Worked solution
Have a go first, then read the solution step by step.
1.Using some doesn't change the concentration: 1900 − 1000 = 900 g is left, still at 20%.
2.Water is 100% − 20% = 80% of it: 900 × 80 ÷ 100 = 720 g. Adding sugar doesn't change the water.
3.After adding sugar, the water is 100% − 36% = 64%: the solution weighs 720 × 100 ÷ 64 = 1125 g.
4.Sugar to add = 1125 − 900 = 225 g.
5.Check: the sugar goes from 180 g to 180 + 225 = 405 g, and 405 × 100 ÷ 1125 = 36 ✓
⚠️Common mistake: keeping the total fixed and working out 900 × (36 − 20) ÷ 100 = 144. The added sugar makes the solution heavier too; what stays the same is the water.
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