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There are two vessels in which alcohol and water are in the ratio of 77 : 23 and 9 : 1 respectively. After mixing the two mixture in certain ratio a new mixture form having alcohol and water in the ratio of 4 : 1. Find in which ratio the two mixture mixed?
  • a)
    5 : 2
  • b)
    10 : 3
  • c)
    3 : 10
  • d)
    2 : 5
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There are two vessels in which alcohol and water are in the ratio of 7...
GIVEN:
Ratio of wine and water in two vessels = 77 : 23 and 9 : 1 respectively
New ratio of wine and water = 4 : 1
CALCULATION:
Let that from first vessel x litre is taken and from second vessel y litre is taken.
Total alcohol in the mixture = (77/100) × (x) + (9/10) × y
⇒ (4/5) × (x + y) = (77x + 90y)/100
⇒ (4x + 4y)/5 = (77x + 90y)/100
⇒ 400x + 400y = (385x + 450y)
⇒ 15x = 50y
∴ x/y = 10/3
Alternative method:
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Most Upvoted Answer
There are two vessels in which alcohol and water are in the ratio of 7...
Given Data:
- Vessel 1: Alcohol and water in the ratio of 77 : 23
- Vessel 2: Alcohol and water in the ratio of 9 : 1
- Final Mixture: Alcohol and water in the ratio of 4 : 1

Let's assume:
- Vessel 1 contains 77x units of alcohol and 23x units of water
- Vessel 2 contains 9y units of alcohol and 1y unit of water
- Final mixture contains 4z units of alcohol and 1z unit of water

Alcohol Quantity Equation:
- From Vessel 1: 77x
- From Vessel 2: 9y
- Total alcohol in the final mixture: 4z

Water Quantity Equation:
- From Vessel 1: 23x
- From Vessel 2: y
- Total water in the final mixture: z

Equating alcohol and water quantities:
- 77x + 9y = 4z (Equation 1)
- 23x + y = z (Equation 2)

Solving the equations:
- Multiply Equation 2 by 4: 92x + 4y = 4z (Equation 3)
- Subtract Equation 3 from Equation 1: 77x + 9y - 92x - 4y = 0
- -15x + 5y = 0
- 3x = y

Ratio of mixing the two mixtures:
- From Equation 2: 23x + 3x = z
- 26x = z
- The ratio of mixing = 26 : 1 = 26/1 = 26
Therefore, the two mixtures were mixed in the ratio of 26 : 1, which is equivalent to option B (10 : 3).
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There are two vessels in which alcohol and water are in the ratio of 77 : 23 and 9 : 1 respectively. After mixing the two mixture in certain ratio a new mixture form having alcohol and water in the ratio of 4 : 1. Find in which ratio the two mixture mixed?a)5 : 2b)10 : 3c)3 : 10d)2 : 5Correct answer is option 'B'. Can you explain this answer?
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