200 litres of mixture contains 15% water and the rest is milk. The amount of milk that must be added so that the resulting mixture contains 87.5 % milk is:Choices:- 30 35 40 45

First, let's find out how much milk and water is there in the initial 200 litres of mixture.

Given that the mixture contains 15% water, it means it contains 85% milk because the total percentage for the mixture is 100%.

So, the amount of milk in the mixture is 85/100 * 200 = 170 litres And the amount of water in the mixture is 15/100 * 200 = 30 litres

Now, we want to add some milk to this mixture so that the resulting mixture contains 87.5% milk. Let's assume that the amount of milk to be added is x litres.

So, the total amount of milk in the new mixture will be 170 + x litres and the total volume of the new mixture will be 200 + x litres.

According to the problem, the percentage of milk in the new mixture should be 87.5%. So, we can set up the following equation:

(170 + x) / (200 + x) = 87.5/100

Solving this equation for x gives us x = 40 litres.

So, 40 litres of milk must be added to the mixture to get a new mixture that contains 87.5% milk.

Therefore, the correct choice is 40.

The problem can be solved in the following steps:

1. First, we need to find out how much milk is currently in the 200 litres of mixture. Since the mixture contains 15% water, it means it contains 85% milk. So, the amount of milk in the mixture is 85% of 200 litres = 170 litres.

2. We are asked to find out how much more milk needs to be added so that the mixture contains 87.5% milk. Let's assume that the amount of milk to be added is x litres.

3. After adding x litres of milk, the total volume of the mixture becomes (200 + x) litres. According to the problem, this new mixture is 87.5% milk.

4. Therefore, the total amount of milk in the new mixture is 170 litres (already present) + x litres (added) = (87.5/100) * (200 + x) litres.

5. Solving the above equation for x gives us the amount of milk that needs to be added.

Let's solve it:

170 + x = 0.875 * (200 + x) 170 + x = 175 + 0.875x 0.125x = 5 x = 5 / 0.125 x = 40 litres

So, 40 litres of milk must be added to the mixture to make it 87.5% milk. Therefore, the correct answer is 40.