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Ratio · change after adding water
P6 · Ratio · PSLE Maths
Question
Raju made a jug of sweet drink by mixing sugar and water. The ratio of the mass of sugar to the mass of water was 5 : 7. He then added 330 g of water, and the ratio became 2 : 5. What was the mass of the sweet drink at first?
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Hint
Only water is added, so the mass of sugar does not change. First make the sugar units the same in both ratios.
Show the answer and step-by-step explanation
Answer: Mass of sweet drink at first 720 g
- Find unchanged — Only water is added, so the mass of sugar is unchanged. First, make the sugar units the same in both ratios.
- Draw model — Draw the sugar as 10 units in both bars. The water is 14 units at first and 25 units after adding water.
- Compare water — The water changes from 14 units to 25 units. The increase in water is 25 − 14 = 11 units.
- Find 1 unit — These 11 units of water are the 330 g added. So 1 unit = 330 ÷ 11 = 30 g.
- Find original mass — At first, there were 10 units of sugar and 14 units of water, making 24 units in all. 24 × 30 = 720 g. 📌 Key idea: when only one quantity changes, first find the unchanged quantity, make its units the same in both ratios, then use the change in units to find 1 unit.
Method: For ratio change questions, first find the unchanged quantity. Here, the sugar is unchanged. Make the sugar units the same in both ratios, then match the increase in water units to the water added.
Practice: 3 similar questions
- Ali made a jug of orange drink. The ratio of the mass of sugar to the mass of water was 2 : 3. After he added 180 g of water, the ratio became 1 : 3. What was the mass of the drink at first?
Answer
300 g — At first, sugar : water = 2 : 3. After adding water, 1 : 3 = 2 : 6. The water increased by 6 − 3 = 3 units, which is 180 g. 1 unit = 180 ÷ 3 = 60 g. The original total was 2 + 3 = 5 units. The mass of the drink at first was 5 × 60 = 300 g.
- Mei Ling made some sweetened lemon tea. The ratio of the mass of sugar to the mass of water was 4 : 9. After she added 270 g of water, the ratio became 2 : 9. What was the mass of the sweetened lemon tea at first?
Answer
390 g — At first, sugar : water = 4 : 9. After adding water, 2 : 9 = 4 : 18. The water increased by 18 − 9 = 9 units, which is 270 g. 1 unit = 270 ÷ 9 = 30 g. The original total was 4 + 9 = 13 units. The mass of the sweetened lemon tea at first was 13 × 30 = 390 g.
- Siti prepared a jug of sweet drink for a class party. The ratio of the mass of sugar to the mass of water was 3 : 4. After she added 280 g of water, the ratio became 2 : 5. What was the mass of the sweet drink at first?
Answer
560 g — At first, 3 : 4 = 6 : 8. After adding water, 2 : 5 = 6 : 15. The water increased by 15 − 8 = 7 units, which is 280 g. 1 unit = 280 ÷ 7 = 40 g. The original total was 6 + 8 = 14 units. The mass of the sweet drink at first was 14 × 40 = 560 g.
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