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Two vessels of equal capacity contains juice and water in the ratio of 5 ∶ 1 and 5 ∶ 7 respectively. The mixture of both the vessels are mixed and transferred into a bigger vessel. What is the ratio of juice and water in the new mixture?
- a)3 ∶ 2
- b)5 ∶ 3
- c)5 ∶ 4
- d)1 ∶ 2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two vessels of equal capacity contains juice and water in the ratio of...
Let both the vessels have ‘a’ litres of mixtures
Total quantity of juice = (5a/6 + 5a/12) = 15a/12
Total quantity of water = (a/6 + 7a/12) = 9a/12
∴ Required ratio = 15a/12 ∶ 9a/12 = 5 ∶ 3
Total quantity of juice = (5a/6 + 5a/12) = 15a/12
Total quantity of water = (a/6 + 7a/12) = 9a/12
∴ Required ratio = 15a/12 ∶ 9a/12 = 5 ∶ 3
Most Upvoted Answer
Two vessels of equal capacity contains juice and water in the ratio of...
Given:
- Two vessels contain juice and water in the ratio of 5:1 and 5:7 respectively.
- The capacity of both vessels is equal.
To find:
- The ratio of juice and water in the new mixture.
Solution:
Let's assume the capacity of each vessel is 'x' units.
Step 1: Calculate the quantities of juice and water in each vessel:
Vessel 1:
- Juice quantity = (5/6) * x
- Water quantity = (1/6) * x
Vessel 2:
- Juice quantity = (5/12) * x
- Water quantity = (7/12) * x
Step 2: Combine the quantities of juice and water from both vessels:
- Total juice quantity = (5/6) * x + (5/12) * x = (10/12) * x + (5/12) * x = (15/12) * x
- Total water quantity = (1/6) * x + (7/12) * x = (2/12) * x + (7/12) * x = (9/12) * x
Step 3: Simplify the ratio of juice and water in the new mixture:
- Ratio of juice to water = (15/12) * x : (9/12) * x = 15x : 9x
Step 4: Simplify the ratio to its simplest form:
- Divide both terms of the ratio by the greatest common divisor (GCD) of 15x and 9x, which is 3x.
- Simplified ratio = (15x/3x) : (9x/3x) = 5 : 3
Therefore, the ratio of juice to water in the new mixture is 5:3, which corresponds to option B.
- Two vessels contain juice and water in the ratio of 5:1 and 5:7 respectively.
- The capacity of both vessels is equal.
To find:
- The ratio of juice and water in the new mixture.
Solution:
Let's assume the capacity of each vessel is 'x' units.
Step 1: Calculate the quantities of juice and water in each vessel:
Vessel 1:
- Juice quantity = (5/6) * x
- Water quantity = (1/6) * x
Vessel 2:
- Juice quantity = (5/12) * x
- Water quantity = (7/12) * x
Step 2: Combine the quantities of juice and water from both vessels:
- Total juice quantity = (5/6) * x + (5/12) * x = (10/12) * x + (5/12) * x = (15/12) * x
- Total water quantity = (1/6) * x + (7/12) * x = (2/12) * x + (7/12) * x = (9/12) * x
Step 3: Simplify the ratio of juice and water in the new mixture:
- Ratio of juice to water = (15/12) * x : (9/12) * x = 15x : 9x
Step 4: Simplify the ratio to its simplest form:
- Divide both terms of the ratio by the greatest common divisor (GCD) of 15x and 9x, which is 3x.
- Simplified ratio = (15x/3x) : (9x/3x) = 5 : 3
Therefore, the ratio of juice to water in the new mixture is 5:3, which corresponds to option B.
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Two vessels of equal capacity contains juice and water in the ratio of 5 ∶ 1 and 5 ∶ 7 respectively. The mixture of both the vessels are mixed and transferred into a bigger vessel. What is the ratio of juice and water in the new mixture?a)3 ∶ 2b)5 ∶ 3c)5 ∶ 4d)1 ∶ 2Correct answer is option 'B'. Can you explain this answer?
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