One year ago, the ratio of the ages of Mike and Jane was 4 : 5. One year hence, the ratio of their ages will be 5 : 6. The present age of Jane is:  Ops:   A. 11 years    B. 12 years    C. 10 years    D. 14 years

Let's solve this step by step:

Step 1: Let's assume the present ages of Mike and Jane are 4x and 5x respectively.

Step 2: According to the problem, one year ago, the ratio of their ages was 4:5. So, we can write it as (4x-1)/(5x-1) = 4/5.

Step 3: Simplifying this equation, we get 20x - 5 = 16x - 4. Solving for x, we get x = 1/4.

Step 4: Substituting x = 1/4 in 5x (Jane's present age), we get Jane's present age as 5*(1/4) = 1.25 years.

However, this doesn't match any of the options given. There seems to be a mistake in the problem.

Let's try a different approach:

Step 1: According to the problem, one year hence, the ratio of their ages will be 5:6. So, let's assume the future ages of Mike and Jane are 5y and 6y respectively.

Step 2: So, their present ages would be 5y-1 and 6y-1 respectively.

Step 3: One year ago, their ages would be 5y-2 and 6y-2 respectively. According to the problem, the ratio of their ages one year ago was 4:5. So, we can write it as (5y-2)/(6y-2) = 4/5.

Step 4: Simplifying this equation, we get 25y - 10 = 24y - 8. Solving for y, we get y = 2.

Step 5: Substituting y = 2 in 6y-1 (Jane's present age), we get Jane's present age as 6*2 - 1 = 11 years.

So, the present age of Jane is 11 years. The correct option is A. 11 years.