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The ratio of the volume of three buckets is 3 : 4 : 5. Buckets contains the mixture of water and alcohol. If the mixture contains water and alcohol in the ratio 1 : 4, 1: 3 and 2 : 5, respectively then find the ratio of water and alcohol when the mixture in all containers are poured in fourth container.
  • a)
    35 : 57
  • b)
    53:157
  • c)
    157 : 53
  • d)
    35 : 157
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The ratio of the volume of three buckets is 3 : 4 : 5. Buckets contain...
Given information:
- The ratio of the volume of three buckets is 3 : 4 : 5.
- The mixture in bucket 1 contains water and alcohol in the ratio 1 : 4.
- The mixture in bucket 2 contains water and alcohol in the ratio 1 : 3.
- The mixture in bucket 3 contains water and alcohol in the ratio 2 : 5.

To find:
- The ratio of water and alcohol when the mixture in all containers are poured into the fourth container.

Solution:
Let's assume the volumes of the three buckets to be 3x, 4x, and 5x, respectively. Therefore, the total volume of the mixture in all three buckets is 12x.

Bucket 1:
In bucket 1, the ratio of water and alcohol is 1 : 4. Therefore, out of 5 parts, 1 part is water and 4 parts are alcohol.

- Water in bucket 1 = (1/5) * 3x = 3x/5
- Alcohol in bucket 1 = (4/5) * 3x = 12x/5

Bucket 2:
In bucket 2, the ratio of water and alcohol is 1 : 3. Therefore, out of 4 parts, 1 part is water and 3 parts are alcohol.

- Water in bucket 2 = (1/4) * 4x = x
- Alcohol in bucket 2 = (3/4) * 4x = 3x

Bucket 3:
In bucket 3, the ratio of water and alcohol is 2 : 5. Therefore, out of 7 parts, 2 parts are water and 5 parts are alcohol.

- Water in bucket 3 = (2/7) * 5x = 10x/7
- Alcohol in bucket 3 = (5/7) * 5x = 25x/7

Total water and alcohol in all buckets:
- Total water = 3x/5 + x + 10x/7 = 41x/35
- Total alcohol = 12x/5 + 3x + 25x/7 = 157x/35

Ratio of water and alcohol in the final mixture:
- Ratio of water to total mixture = (41x/35) / (41x/35 + 157x/35) = 41/198
- Ratio of alcohol to total mixture = (157x/35) / (41x/35 + 157x/35) = 157/198

Therefore, the ratio of water and alcohol in the final mixture is 41 : 157, which is option (D).
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The ratio of the volume of three buckets is 3 : 4 : 5. Buckets contains the mixture of water and alcohol. If the mixture contains water and alcohol in the ratio 1 : 4, 1: 3 and 2 : 5, respectively then find the ratio of water and alcohol when the mixture in all containers are poured in fourth container.a)35 : 57b)53:157c)157 : 53d)35 : 157Correct answer is option 'D'. Can you explain this answer?
Question Description
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