At present, the ratio between the ages of Arun and Harish is 4:3. After 6 years, the age of Arun will be 26 years. What is the present age of Harish?

Introduction / Context:
This question involves finding one person's present age from a given ratio and a piece of future age information. The present age ratio of Arun and Harish is known, and Arun's age after 6 years is specified. We must compute Harish's present age. Such questions are common in the topic problems on ages and ratios.

Given Data / Assumptions:
The present ratio of the ages of Arun and Harish is 4:3. After 6 years, Arun's age will be 26 years. We are required to find Harish's present age in years. Ages are assumed to be whole numbers.

Concept / Approach:
First, we use the future age of Arun to find his present age by subtracting 6 years. Then we use the ratio 4:3 to find Harish's age. Expressing the ratio as Arun : Harish = 4 : 3 means that Arun's age is 4 parts and Harish's age is 3 parts. Once the value of one part is determined, we can scale the ratio appropriately.

Step-by-Step Solution:
Step 1: After 6 years, Arun's age will be 26 years. Therefore, Arun's present age is 26 - 6 = 20 years.Step 2: The present age ratio Arun : Harish is 4 : 3. So we can write Arun's age as 4k and Harish's age as 3k for some positive number k.Step 3: Since Arun's present age is 20, we have 4k = 20.Step 4: Solve for k: k = 20 / 4 = 5.Step 5: Harish's present age is 3k = 3 * 5 = 15 years.

Verification / Alternative check:
The ages 20 and 15 are in the ratio 20:15, which simplifies to 4:3 when divided by 5, matching the given ratio. After 6 years, Arun will be 26 and Harish will be 21. The question only requires Harish's present age, and the numbers are consistent, confirming the correctness of the solution.

Why Other Options Are Wrong:
If Harish were 16, 18, or 21 years old at present, the corresponding ratios with Arun's age of 20 would be 20:16, 20:18, or 20:21, which simplify to 5:4, 10:9, and approximately 20:21, none of which equal 4:3. Thus, those options do not satisfy the given ratio and must be rejected.

Common Pitfalls:
Some learners mistakenly use Arun's future age of 26 directly in the ratio instead of first converting it to the present age of 20. Another error is to set up the ratio in the reverse order. Correctly identifying whose age corresponds to which part of the ratio and adjusting for the time shift is crucial.

Final Answer:
Harish is 15 years old at present.