The ratio of earnings of A and B is 4 : 5. If the earnings of A increase by 20% and the earnings of B decrease by 20%, the new ratio of their earnings becomes 6 : 5. What are the actual earnings of A?

Introduction:
This question checks how well you reason about ratios and percentage changes without assuming unnecessary numerical values. Sometimes aptitude questions are designed so that a unique numerical answer cannot be found, and the correct response is that the data are insufficient to determine an exact amount.

Given Data / Assumptions:
Original ratio of earnings of A and B is 4 : 5.
Earnings of A increase by 20% from this original value.
Earnings of B decrease by 20% from this original value.
The new ratio of earnings becomes 6 : 5.
We are asked to find the actual earnings of A in rupees.

Concept / Approach:
Let the original earnings of A and B be in the ratio 4 : 5, so we can represent them as 4x and 5x respectively for some positive number x. After applying the stated percentage changes, the new amounts can still be expressed in terms of x. If the new ratio condition holds for all positive values of x, then the actual numerical value of x cannot be uniquely determined based only on this information.

Step-by-Step Solution:
Let original earning of A = 4x. Let original earning of B = 5x. A s earning increases by 20%, so new earning of A = 4x * 1.20 = 4.8x. B s earning decreases by 20%, so new earning of B = 5x * 0.80 = 4x. Compute the new ratio of earnings: new A : new B = 4.8x : 4x. Divide both terms by x to remove the common factor: 4.8 : 4. Simplify 4.8 : 4 by dividing both sides by 0.8, giving 6 : 5. Thus the new ratio condition is automatically satisfied for any positive x. No additional equation is available to determine the value of x.
Verification / Alternative check:
We can try specific values for x. If x = 1000, then original earnings are A = 4000, B = 5000. After the changes, A becomes 4800 and B becomes 4000, giving ratio 4800 : 4000 = 6 : 5. Similarly, if x = 2000, original earnings are A = 8000, B = 10000 and new earnings are A = 9600, B = 8000. The ratio is again 6 : 5. This shows that many different actual earnings values satisfy the given conditions.

Why Other Options Are Wrong:
The numerical values Rs. 22,000, Rs. 26,400, Rs. 27,500, and Rs. 30,000 each correspond to some possible choice of x, but there is no reason to prefer one over another because the problem does not provide any total, difference, or other constraint to fix x. Choosing any specific rupee value would be arbitrary and not supported by the data.

Common Pitfalls:
A common mistake is to assume some convenient value for x and then treat the resulting rupee amounts as uniquely determined. Another error is to misread the question as asking for the ratio of earnings after the change, rather than the actual numerical value of A s earnings. When a question asks for a specific amount, always check whether the information is sufficient to fix all unknowns.

Final Answer:
The actual earnings of A cannot be uniquely determined from the given information, so the correct option is Cannot be determined.