The ratio of the present ages of Raman and Lamba is 7 : 5. After 6 years, the age of Raman will be 48 years. What is the present age, in years, of Lamba?

Introduction / Context:
This is a simple age ratio problem where the future age of one person is given explicitly, and the present age ratio between two people is also provided. Such problems are common in aptitude tests because they can be solved straightforwardly using proportional reasoning and basic arithmetic, without lengthy algebra.

Given Data / Assumptions:

• The present age ratio of Raman and Lamba is 7 : 5.
• After 6 years, Raman age will be 48 years.
• We must determine the present age of Lamba.
• All ages are given in years and are positive.

Concept / Approach:
We model present ages in terms of a common multiple. If Raman present age is 7k and Lamba present age is 5k, then after 6 years Raman will be 7k + 6. Since this is told to be 48 years, we can solve for k directly. Once k is known, we substitute into 5k to find Lamba present age. This technique of representing ages based on ratios is standard for such problems.

Step-by-Step Solution:
Step 1: Let the present age of Raman be 7k years and the present age of Lamba be 5k years. Step 2: After 6 years, Raman age will be 7k + 6 years. Step 3: According to the question, after 6 years Raman age is 48 years, so 7k + 6 = 48. Step 4: Subtract 6 from both sides to get 7k = 42. Step 5: Divide by 7 to find k = 6. Step 6: Lamba present age is 5k years, so it is 5 * 6 = 30 years. Step 7: Therefore the present age of Lamba is 30 years.

Verification / Alternative check:
With k = 6, Raman present age is 7 * 6 = 42 years. After 6 years, Raman will be 42 + 6 = 48 years, which matches the condition given in the question. Lamba present age is 30 years, and their present ratio is 42 : 30 which simplifies to 7 : 5 by dividing both numbers by 6. Thus, both the ratio and the future age condition are satisfied, confirming the correctness of the answer.

Why Other Options Are Wrong:
Option B (25 years) would give a present ratio that does not simplify cleanly to 7 : 5 when paired with Raman correct present age, so it is wrong.
Option C (35 years) would make Lamba too old relative to Raman, and the ratio 42 : 35 does not equal 7 : 5.
Option D (40 years) clearly does not fit the ratio 7 : 5 with Raman present age of 42 years, so it is also incorrect.

Common Pitfalls:
Learners may mistakenly assume that the ratio applies to future ages rather than present ages, which leads to incorrect equations. Another error is to try to guess ages without using a variable, which can be time consuming and unreliable. Always express ratio based ages as multiples of a variable and use the given future or past condition to solve systematically.

Final Answer:
The present age of Lamba is 30 years.