The ratio of A age to B age is 4 : 3. A will be 26 years old after 6 years. What is the present age of B in years?

Introduction / Context:
This is a simple ratio and future age based problem on ages. The current ratio of two ages is given, and a future value for one person age is specified. You must find the current age of the other person. Such questions are excellent practice for connecting present and future ages and for using ratios to derive actual numbers.

Given Data / Assumptions:

• The ratio of the present ages of A and B is 4 : 3.
• A will be 26 years old after 6 years.
• We need to find B present age.
• Both A and B age normally by 6 years over the period.

Concept / Approach:
First determine A present age from the given future age information. Then use the ratio to find B age. Since the ratio 4 : 3 relates the present ages, we can set up a proportion using A present age and solve for B. This avoids the need for introducing an extra variable for the ratio. The method is direct and relies on basic proportional reasoning.

Step-by-Step Solution:
Step 1: A will be 26 years old after 6 years, so A present age is 26 − 6 = 20 years. Step 2: The ratio of the present ages A : B is 4 : 3, meaning A / B = 4 / 3. Step 3: Substitute A = 20 into the ratio to get 20 / B = 4 / 3. Step 4: Solve this proportion to get B = (3 / 4) × 20 = 15 years. Step 5: Hence, the present age of B is 15 years.

Verification / Alternative check:
Check the ratio with the found ages. If A is 20 and B is 15, the ratio 20 : 15 simplifies to 4 : 3 when both numbers are divided by 5, which matches the given ratio. Also, after 6 years, A will indeed be 26 years old, which is consistent with the given future age. Therefore, the solution is correct and satisfies all the conditions of the question.

Why Other Options Are Wrong:
Option 12 years: If B were 12, the ratio would be 20 : 12, which simplifies to 5 : 3, not 4 : 3.
Option 21 years: This gives a ratio of 20 : 21, which is less than 1 and does not simplify to 4 : 3.
Option 13 years and 18 years: These values also do not produce the correct 4 : 3 ratio when paired with A present age of 20 years.

Common Pitfalls:
Learners sometimes forget to subtract the 6 years to find A present age or misapply the ratio by writing 3 : 4 instead of 4 : 3. Another common problem is inverting the fraction incorrectly when solving the proportion. Careful writing of the ratio and systematic cross multiplication help avoid these algebraic mistakes.

Final Answer:
The present age of B is 15 years.