In the mixture of 70 liters, the ratio of milk and water is 3 : 4. If this ratio is changed to 3 : 5, then tell the amount of excess water (in liters) mixed in the mixture.
Question
In the mixture of 70 liters, the ratio of milk and water is 3 : 4. If this ratio is changed to 3 : 5, then tell the amount of excess water (in liters) mixed in the mixture.
Solution 1
Step 1: In the initial mixture, the ratio of milk to water is 3:4. This means that out of every 7 parts of the mixture, 3 parts are milk and 4 parts are water.
Step 2: The total volume of the mixture is 70 liters. So, each part of the mixture is 70/7 = 10 liters.
Step 3: Therefore, the volume of milk in the mixture is 3 parts * 10 liters/part = 30 liters, and the volume of water is 4 parts * 10 liters/part = 40 liters.
Step 4: The ratio of milk to water is changed to 3:5. This means that for every 3 parts of milk, we now have 5 parts of water.
Step 5: The volume of milk remains the same at 30 liters, which is 3 parts. So, each part is now 30/3 = 10 liters.
Step 6: Therefore, the volume of water should be 5 parts * 10 liters/part = 50 liters.
Step 7: The excess water mixed in the mixture is the difference between the new volume of water and the original volume of water, which is 50 liters - 40 liters = 10 liters.
So, 10 liters of water is the excess amount mixed in the mixture.
Solution 2
Step 1: In the initial mixture, the ratio of milk to water is 3:4. This means that out of every 7 parts of the mixture, 3 parts are milk and 4 parts are water.
Step 2: The total volume of the mixture is 70 liters. So, each part of the mixture is 70/7 = 10 liters.
Step 3: Therefore, the volume of milk in the mixture is 3 parts * 10 liters/part = 30 liters, and the volume of water is 4 parts * 10 liters/part = 40 liters.
Step 4: The ratio of milk to water is changed to 3:5. This means that for every 3 parts of milk, we now have 5 parts of water.
Step 5: The volume of milk remains the same at 30 liters, which is 3 parts. So, each part is now 30/3 = 10 liters.
Step 6: Therefore, the volume of water should be 5 parts * 10 liters/part = 50 liters.
Step 7: The excess water mixed in the mixture is the difference between the new volume of water and the original volume of water, which is 50 liters - 40 liters = 10 liters.
So, 10 liters of water is the excess amount mixed in the mixture.
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