The ratio of the present ages of L and N is 7 : 5. If the age of N after seven years will be 32 years, then what is the present age in years of L?

Introduction / Context:
This is a straightforward ratio based problem on ages. It combines a given ratio of present ages with one absolute value for a future age, and from this you have to find one person present age. Such questions check your ability to use a ratio variable, link it with an actual numeric future age, and then scale the ratio correctly. They are very common in aptitude tests because they check conceptual understanding more than heavy calculations.

Given Data / Assumptions:

• The ratio of the present ages of L and N is 7 : 5.
• After 7 years, the age of N will be 32 years.
• We are asked to find the present age of L in years.
• Both people ages increase in a normal way, with the same number of years added over time.

Concept / Approach:
When ages are in a ratio like 7 : 5, we represent the actual ages as multiples of a common variable. Using that representation and any extra condition, such as a known future or past age, we can find the value of the common multiplier. Once that multiplier is known, the present ages follow directly. In this question, we only need one equation because the future age of N is given exactly, and that is enough to compute the variable and then L age.

Step-by-Step Solution:
Step 1: Let the present ages of L and N be 7k and 5k respectively, where k is a positive number. Step 2: After 7 years, N age will be 5k + 7. Step 3: We are told that 5k + 7 equals 32 years. Step 4: Solve 5k + 7 = 32 to obtain 5k = 25 and hence k = 5. Step 5: Substitute k into L age, so L present age is 7k = 7 × 5 = 35 years.

Verification / Alternative check:
Check the ratio using the found ages. If L is 35 and N is 25 at present, the ratio 35 : 25 simplifies to 7 : 5, which matches the given ratio. After 7 years, N age becomes 25 + 7 = 32 years, which is also exactly the future age stated in the question. Therefore the value 35 years for L is fully consistent with all conditions, and the solution is correct.

Why Other Options Are Wrong:
Option 49: If L were 49 years old, N would be 35 years old to keep the 7 : 5 ratio. Then after 7 years, N would be 42, not 32, so this is incorrect.
Option 28: With L as 28, N would be 20. After 7 years, N would be 27, which again does not match 32 years.
Option 42: In this case N would be 30 initially and 37 after 7 years, still not 32.
Option 30: This does not even preserve the ratio of 7 : 5 when paired with any simple value for N, so it fails the first condition itself.

Common Pitfalls:
Students sometimes wrongly add years only to one person or forget to add the same number of years to both when dealing with future ages. Another frequent mistake is to directly treat 7 and 5 as ages instead of as ratio parts. Always express the actual ages as 7k and 5k, then use the extra information to find k. Checking the ratio at the end is a good habit to avoid careless slips.

Final Answer:
The present age of L is 35 years.