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 10 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 10 liters?
1:3
1:2
1:4
1:5
Initial sugar = 1 part, water = 4 parts. Total = 5 parts. New sugar = 2 liters, water = 8 liters. Ratio = 2:8 = 1:4.
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 10 liters?
Solution: Initial sugar = 1 part, water = 4 parts. Total = 5 parts. New sugar = 2 liters, water = 8 liters. Ratio = 2:8 = 1:4.
Steps: 10
Step 1: Understand the initial ratio of sugar to water, which is 1:4.
Step 2: This means for every 1 part of sugar, there are 4 parts of water.
Step 3: Calculate the total parts in the mixture: 1 part (sugar) + 4 parts (water) = 5 parts.
Step 4: Since the total volume of the mixture is 10 liters, find out how much sugar and water are in the mixture.
Step 5: Calculate the volume of sugar: (1 part / 5 parts) * 10 liters = 2 liters of sugar.
Step 6: Calculate the volume of water: (4 parts / 5 parts) * 10 liters = 8 liters of water.
Step 7: Now, add 2 liters of sugar to the existing 2 liters of sugar, making the new sugar volume 4 liters.
Step 8: The volume of water remains the same at 8 liters.
Step 9: Now, find the new ratio of sugar to water: 4 liters of sugar to 8 liters of water.
Step 10: Simplify the ratio: 4:8 can be simplified to 1:2.
