From a cask of milk containing 30 litres, 6 litres are drawn out and the cask is filled up with water. If the same process is repeated a second, then a third time, what will be the number of litres of milk left in the cask?Options :0.512 liter12 liters14.38 liters15.36 liters

The problem involves a series of dilutions. Here's how you can solve it:

1. Start with 30 litres of milk.
2. After the first operation, 6 litres of milk are removed. This leaves 30 - 6 = 24 litres of milk. The cask is then filled up with water, so the total volume in the cask remains 30 litres.
3. The milk now makes up 24/30 = 0.8 (or 80%) of the total liquid in the cask.
4. After the second operation, again 6 litres of the liquid (which is 80% milk and 20% water) are removed. This means 0.8 * 6 = 4.8 litres of milk are removed, leaving 24 - 4.8 = 19.2 litres of milk. The cask is then filled up with water, so the total volume in the cask remains 30 litres.
5. The milk now makes up 19.2/30 = 0.64 (or 64%) of the total liquid in the cask.
6. After the third operation, again 6 litres of the liquid (which is 64% milk and 36% water) are removed. This means 0.64 * 6 = 3.84 litres of milk are removed, leaving 19.2 - 3.84 = 15.36 litres of milk. The cask is then filled up with water, so the total volume in the cask remains 30 litres.

So, the answer is 15.36 litres of milk left in the cask.

The problem involves a series of dilutions. Here's how you can solve it:

1. Start with 30 litres of milk.

2. After the first operation, 6 litres of milk are removed. This leaves 30 - 6 = 24 litres of milk. The cask is then filled up with water, but the total volume remains 30 litres. So, the proportion of milk in the cask is now 24/30 = 0.8 (or 80%).

3. The same operation is repeated. This time, 6 litres of the mixture (which is 80% milk) are removed. This means 6 * 0.8 = 4.8 litres of milk are removed, leaving 24 - 4.8 = 19.2 litres of milk. Again, the cask is filled up with water, and the new proportion of milk is 19.2/30 = 0.64 (or 64%).

4. The operation is repeated a third time. Now, 6 litres of the mixture (which is 64% milk) are removed. This means 6 * 0.64 = 3.84 litres of milk are removed, leaving 19.2 - 3.84 = 15.36 litres of milk.

So, the answer is 15.36 litres of milk left in the cask.