There are three bottles of mixture of milk and water of ratios 3 : 5, 7 : 5 and 6 : 5. 16 litres of the first and 22 litres of the third bottles are taken. How much quantity from second bottle is to be taken so that final mixture from three bottles will be of ratios 16 : 15?Options22 litres24 litres10 litres20 litres

The problem is asking for the amount of the second mixture needed to achieve a final mixture ratio of 16:15 when 16 litres of the first mixture and 22 litres of the third mixture are used.

First, let's understand the ratios:

1. The first mixture has a ratio of 3:5, which means for every 3 parts of milk, there are 5 parts of water.
2. The second mixture has a ratio of 7:5, which means for every 7 parts of milk, there are 5 parts of water.
3. The third mixture has a ratio of 6:5, which means for every 6 parts of milk, there are 5 parts of water.

The final mixture should have a ratio of 16:15, which means for every 16 parts of milk, there should be 15 parts of water.

Now, let's calculate the amount of milk and water in the first and third mixtures:

1. In the first mixture, out of 16 litres, 16*(3/8) = 6 litres is milk and 16*(5/8) = 10 litres is water.
2. In the third mixture, out of 22 litres, 22*(6/11) = 12 litres is milk and 22*(5/11) = 10 litres is water.

So, the total amount of milk is 6 + 12 = 18 litres and the total amount of water is 10 + 10 = 20 litres.

Let's denote the amount of the second mixture to be taken as x litres. Then, the amount of milk in the second mixture is x*(7/12) and the amount of water is x*(5/12).

The final mixture should have a ratio of 16:15, so the total amount of milk to the total amount of water should be 16:15. Therefore, we can set up the following equation:

(18 + x*(7/12)) / (20 + x*(5/12)) = 16/15

Solving this equation for x gives x = 20 litres. Therefore, 20 litres of the second mixture should be taken to achieve the final mixture ratio of 16:15. So, the answer is 20 litres.