The ratio of the present ages of Rasika and Shami is 7 : 5. After 17 years the ratio of their ages will be 12 : 11. What is Rasika present age in years?

Introduction / Context:
This question is a classic two time ratio problem on ages. It gives the ratio of present ages and the ratio of ages after a certain number of years. From these two ratios you must determine the actual present age of one person. Such questions help test algebraic skills, especially forming equations from ratios and understanding how adding a constant number of years affects both numerator and denominator in an age ratio.

Given Data / Assumptions:

• The present age ratio of Rasika to Shami is 7 : 5.
• After 17 years, the ratio of their ages will be 12 : 11.
• We are asked to find the present age of Rasika.
• Both Rasika and Shami age in a normal way, each gaining 17 years over the given period.

Concept / Approach:
When a problem gives the ratio of present ages and another ratio many years later, the standard method is to represent the present ages using a common variable, and then write an equation for the future ratio. The future ratio expression will involve the same variable plus the added years. Solving this equation yields the value of the variable and thus the actual ages. This approach works because age is linear with time and both ages increase by the same constant amount over the same period.

Step-by-Step Solution:
Step 1: Let the present ages of Rasika and Shami be 7k and 5k respectively. Step 2: After 17 years, Rasika age becomes 7k + 17 and Shami age becomes 5k + 17. Step 3: According to the question, the ratio (7k + 17) : (5k + 17) is equal to 12 : 11. Step 4: Form the equation (7k + 17) / (5k + 17) = 12 / 11 and solve this linear equation for k. Step 5: Solving gives k = 1, so Rasika present age is 7k = 7 years.

Verification / Alternative check:
If Rasika is 7 years old at present, then Shami current age is 5 years. After 17 years, Rasika age will be 7 + 17 = 24 years and Shami age will be 5 + 17 = 22 years. The ratio 24 : 22 simplifies to 12 : 11, which exactly matches the future ratio given in the question. Therefore, the derived value of 7 years is fully consistent with the data, even though it may look small for a typical person name, the mathematics is correct for the puzzle.

Why Other Options Are Wrong:
Option 5: If Rasika were 5 years old, Shami would be about 3.57 years old from the ratio, which does not yield a neat future ratio of 12 : 11 when 17 years are added.
Option 80: This would make Shami age large as well, and the resulting future ratio would not be 12 : 11.
Option 16: If Rasika age were 16, Shami age would be 16 × 5 ÷ 7 which is not an integer, and the future ratio would not match.
Option 28: Similar tests show that this does not preserve the stated ratios either.

Common Pitfalls:
Learners sometimes mix up which person corresponds to which part of the ratio or forget that 17 years must be added to both ages in the future scenario. Another common mistake is to treat 7 and 5 as actual ages instead of 7k and 5k, which prevents you from satisfying both present and future ratios simultaneously. Always set up a clean fraction equation and cross multiply carefully to avoid algebraic slips.

Final Answer:
Rasika present age is 7 years.