A 40 litre mixture contains milk and water in the ratio of 3:2. 20 lit...
Answer – d) 9:1 Explanation : milk = 40*3/5 = 24 and water = 16 litres initially milk = 24 – 20*3/5 + 20 = 32 – 20*4/5 + 20 = 36 water = 16 – 20*2/5 = 8 – 20*1/5 = 4
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A 40 litre mixture contains milk and water in the ratio of 3:2. 20 lit...
Problem: A 40 litre mixture contains milk and water in the ratio of 3:2. 20 litres of the mixture is drawn of and filled with pure milk. This operation is repeated one more time. At the end what is the ratio of milk and water in the resulting mixture?
Solution:
Given:
- A 40 litre mixture contains milk and water in the ratio of 3:2.
- 20 litres of the mixture is drawn of and filled with pure milk.
- This operation is repeated one more time.
To find: The ratio of milk and water in the resulting mixture.
Let's solve this problem step by step:
Step 1:
The initial ratio of milk and water in the mixture is 3:2.
- Let the quantity of milk be 3x litres.
- Let the quantity of water be 2x litres.
Therefore, the total quantity of the mixture is 5x litres.
Given, the total quantity of mixture = 40 litres.
Therefore,
5x = 40
=> x = 8
So, the quantity of milk in the mixture = 3x = 24 litres
And the quantity of water in the mixture = 2x = 16 litres
Step 2:
20 litres of the mixture is drawn of and filled with pure milk.
- 20 litres of the mixture contains,
- 20 * (3/5) = 12 litres of milk
- 20 * (2/5) = 8 litres of water
- Filled with pure milk, which contains 20 litres of milk.
After first step, the total quantity of the mixture = 40 - 20 + 20 = 40 litres
And the quantity of milk in the mixture = 24 - 12 + 20 = 32 litres
And the quantity of water in the mixture = 16 - 8 = 8 litres
Step 3:
20 litres of the mixture is drawn of and filled with pure milk.
- 20 litres of the mixture contains,
- 20 * (3/5) = 12 litres of milk
- 20 * (2/5) = 8 litres of water
- Filled with pure milk, which contains 20 litres of milk.
After second step, the total quantity of the mixture = 40 - 20 + 20 = 40 litres
And the quantity of milk in the mixture = 32 - 12 + 20 = 40 litres
And the quantity of water in the mixture = 8 - 8 = 0 litres
Therefore, the ratio of milk and water in the resulting mixture is 40:0 = 9:1.
Hence, the correct option is (d) 9:1.