The present ages of Rangana and Sayed are in the ratio 7 : 5. After 11 years, the ratio of their ages will become 4 : 3. What is the present age, in years, of Rangana?

Introduction / Context:
This question is a typical example of age ratio problems where the ratio of ages is given at the present time and at a future time. Such problems are designed to check your ability to translate ratios and time shifts into linear equations and then solve for actual ages. This pattern appears frequently in aptitude exams because it combines proportional reasoning with basic algebra.

Given Data / Assumptions:

• The present age ratio of Rangana and Sayed is 7 : 5.
• After 11 years, the ratio of their ages will become 4 : 3.
• We must find the present age of Rangana in years.
• All ages are expressed in years and are positive integers.

Concept / Approach:
When ages are given in ratio form, we can represent them as multiples of a common variable. Time shifts such as “after 11 years” are handled by adding 11 to each person age expression. Setting the future ratio equal to the given fraction produces an equation in the common variable. Solving that equation gives the actual ages. This method avoids guesswork and ensures a systematic solution.

Step-by-Step Solution:
Step 1: Let the present age of Rangana be 7x years and the present age of Sayed be 5x years, where x is a positive constant. Step 2: After 11 years, Rangana age will be 7x + 11 years. Step 3: After 11 years, Sayed age will be 5x + 11 years. Step 4: At that time the ratio of their ages is given as 4 : 3, so (7x + 11) / (5x + 11) = 4 / 3. Step 5: Cross multiply to clear the fraction: 3 * (7x + 11) = 4 * (5x + 11). Step 6: Expand both sides: 21x + 33 = 20x + 44. Step 7: Rearrange terms: 21x - 20x = 44 - 33, so x = 11. Step 8: Substitute back to find Rangana present age: 7x = 7 * 11 = 77 years. Step 9: Therefore, the present age of Rangana is 77 years.

Verification / Alternative check:
Check the result by computing future ages. If x = 11, Sayed present age is 5 * 11 = 55 years. After 11 years, Rangana will be 77 + 11 = 88 years and Sayed will be 55 + 11 = 66 years. The ratio 88 : 66 simplifies by dividing both numbers by 22 to give 4 : 3, exactly matching the condition in the question. Hence the answer is verified as correct.

Why Other Options Are Wrong:
Option A (55 years) would make Sayed age too small compared to the required ratio, and the future ratio would not turn into 4 : 3.
Option C (70 years) does not satisfy the future ratio when combined with a consistent age for Sayed, so it is not valid.
Option D (96 years) leads to a future ratio that deviates significantly from 4 : 3, so this option is also incorrect.

Common Pitfalls:
Learners sometimes incorrectly add 11 only to one age in the ratio instead of to both. Another mistake is to treat the ratio values as direct ages without introducing a variable multiple. Always represent ratio based ages as multiples of a common variable and then apply the time shift to all people involved. Cross multiplying carefully avoids algebraic errors and leads to a clean solution.

Final Answer:
The present age of Rangana is 77 years.