If the ratio of milk and water in a mixture is 7: 5. We withdraw 9 lt mixture and added same quantity of water to the mixture, then ratio becomes 1: 1. Find initial quantity of milk.A] 36.75 lt B] 22.15 lt C] 17.50 lt D] 21.35 ltOptions :ABCD

Let's solve this step by step:

Step 1: Let's assume the initial quantity of the mixture is 'x' litres. According to the problem, the ratio of milk to water in this mixture is 7:5. This means that the quantity of milk is (7/12)*x and the quantity of water is (5/12)*x.

Step 2: Now, 9 litres of this mixture is removed. So, the quantity of milk and water removed will be in the same ratio of 7:5. Therefore, (7/12)*9 litres of milk is removed and (5/12)*9 litres of water is removed.

Step 3: After removing, the remaining quantity of milk in the mixture is (7/12)*x - (7/12)*9 and the remaining quantity of water is (5/12)*x - (5/12)*9.

Step 4: Now, 9 litres of water is added to the mixture. So, the new quantity of water becomes (5/12)*x - (5/12)*9 + 9.

Step 5: According to the problem, after this operation, the ratio of milk to water becomes 1:1. This means the quantity of milk is equal to the quantity of water. So, we can set up the following equation:

(7/12)*x - (7/12)*9 = (5/12)*x - (5/12)*9 + 9

Step 6: Solving this equation will give us the value of 'x', which is the initial quantity of the mixture. After finding 'x', we can substitute it back into the equation (7/12)*x to find the initial quantity of milk.

Let's solve the equation:

(7/12)*x - (7/12)*9 = (5/12)*x - (5/12)*9 + 9

Solving this equation gives x = 36 litres.

Substituting x = 36 litres into the equation (7/12)*x gives the initial quantity of milk = (7/12)*36 = 21 litres.

So, the initial quantity of milk is 21 litres. The closest option to this is D] 21.35 lt.