In a certain mixture, the ratio of sugar to water is 1:4. If 2 liters of sugar is added, what will be the new ratio if the total volume of the mixture is 20 liters?
Practice Questions
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Q1
In a certain mixture, the ratio of sugar to water is 1:4. If 2 liters of sugar is added, what will be the new ratio if the total volume of the mixture is 20 liters?
1:3
1:4
1:5
1:6
Initially, there is 1 part sugar and 4 parts water, totaling 5 parts. In 20 liters, there are 4 liters of sugar and 16 liters of water. After adding 2 liters of sugar, the new ratio is 6:16, which simplifies to 1:5.
Questions & Step-by-step Solutions
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Q
Q: In a certain mixture, the ratio of sugar to water is 1:4. If 2 liters of sugar is added, what will be the new ratio if the total volume of the mixture is 20 liters?
Solution: Initially, there is 1 part sugar and 4 parts water, totaling 5 parts. In 20 liters, there are 4 liters of sugar and 16 liters of water. After adding 2 liters of sugar, the new ratio is 6:16, which simplifies to 1:5.
Steps: 10
Step 1: Understand the initial ratio of sugar to water, which is 1:4.
Step 2: Calculate the total parts in the mixture. 1 part sugar + 4 parts water = 5 parts.
Step 3: Determine how much sugar and water is in the 20 liters based on the ratio.
Step 4: Calculate the amount of sugar: (1 part / 5 parts) * 20 liters = 4 liters of sugar.
Step 5: Calculate the amount of water: (4 parts / 5 parts) * 20 liters = 16 liters of water.
Step 6: Add 2 liters of sugar to the existing 4 liters of sugar. Now, there are 4 + 2 = 6 liters of sugar.
Step 7: The amount of water remains the same at 16 liters.
Step 8: Write the new ratio of sugar to water: 6 liters of sugar to 16 liters of water.
Step 9: Simplify the ratio 6:16 by dividing both numbers by 2, which gives 3:8.
Step 10: The final simplified ratio of sugar to water is 3:8.
