Person A is two years older than person B, and B is twice as old as person C. If the total of the present ages of A, B and C is 27 years, then how old is B now?

Introduction / Context:
This age puzzle involves three related people, where the ages are connected by simple linear relationships. One person is older than another by a fixed number of years, and one is a multiple of someone else age. The sum of all three present ages is given. Questions like this are very common in aptitude exams and practice tests because they combine logical reasoning with elementary algebra and test whether you can set up and solve equations with several variables.

Given Data / Assumptions:

• Person A is two years older than person B.
• Person B is twice as old as person C.
• The total of the present ages of A, B and C is 27 years.
• We have to determine the present age of person B.
• All ages are present ages, and we do not deal with past or future times.

Concept / Approach:
The best way to handle this question is to introduce a variable for the simplest age, which is usually the youngest person. Here the age of C is the natural choice. Then we express B as twice that variable and A as B plus two years. This gives three expressions for each person age in terms of the same variable. Summing them and equating to the total age leads to a single linear equation that is easy to solve. Once the variable is found, B age follows directly, and we can verify by checking the total and the relationships.

Step-by-Step Solution:
Step 1: Let the present age of C be c years. Step 2: Since B is twice as old as C, B present age is 2c years. Step 3: A is two years older than B, so A present age is 2c + 2 years. Step 4: The total of their ages is A + B + C = (2c + 2) + 2c + c, which simplifies to 5c + 2. Step 5: Given that the total is 27, we set 5c + 2 = 27 and solve for c to get c = 5 years. Step 6: Then B present age is 2c = 10 years, which is the required answer.

Verification / Alternative check:
Using the values we found, C is 5 years old, B is 10 years old, and A is 12 years old. Add them: 5 + 10 + 12 = 27, which matches the total given in the problem. Also check the relationships: B is twice C because 10 = 2 × 5, and A is two years older than B because 12 = 10 + 2. Both conditions are satisfied, so the solution is correct and consistent with all parts of the question.

Why Other Options Are Wrong:
Option 11 yrs: If B were 11, C would be 5.5 and the total would not come to 27, so this is not acceptable under the usual whole number age assumption.
Option 12 yrs: This would give a different distribution of ages that does not match the total or the twice relationship exactly.
Option 13 yrs and Option 9 yrs: Similar checks show that they produce sums or relations that are inconsistent with the given conditions, so they cannot be correct.

Common Pitfalls:
A typical mistake is to choose the wrong person for the variable or to forget that A is older than B by 2 years, not the other way around. Some learners also incorrectly add or subtract ages when setting up the sum. A clear strategy is to write each age in terms of the youngest person, sum them carefully, and double check that all relationships are respected. Drawing a quick age diagram can also help avoid confusion.

Final Answer:
The present age of person B is 10 years (that is, option 10 yrs).