Mr. Ramesh has three daughters namely Rohini, Anita and Keerthi. Rohin...
Square numbers – a, b, c
(a + 5) + (b + 5)+ (c + 5) = 44
a + b + c = 44 – 15 = 29
Possible values of a, b, c = 4, 9, 16 [Out of 1, 4, 9, 16, 25] The age of Rohini and Anita after two years = 29; The age of Rohini and Keerthi after four years = 28
Mr. Ramesh has three daughters namely Rohini, Anita and Keerthi. Rohin...
Understanding the Problem
To solve the problem, we need to determine the ages of Mr. Ramesh's daughters, which are square numbers, and analyze the quantities given.
Identifying the Ages
1. The ages of the daughters are square numbers:
- Possible square numbers for ages under 20: 0, 1, 4, 9, 16.
- Since Rohini is the eldest and Keerthi is the youngest, let's denote their ages as:
- Rohini (R) = x^2
- Anita (A) = y^2
- Keerthi (K) = z^2
2. The sum of their ages after 5 years is 44:
- (R + 5) + (A + 5) + (K + 5) = 44
- R + A + K + 15 = 44
- R + A + K = 29
Finding Valid Combinations
- We need to find combinations of R, A, and K that are square numbers and add up to 29.
- The valid combinations given the constraints are:
- R = 16, A = 9, K = 4
- R = 16, A = 4, K = 9 (not valid since R must be eldest)
Thus, we have:
- Rohini: 16 years
- Anita: 9 years
- Keerthi: 4 years
Calculating the Quantities
- Quantity I: Age of Rohini and Anita after 2 years:
- Rohini: 16 + 2 = 18
- Anita: 9 + 2 = 11
- Total: 18 + 11 = 29
- Quantity II: Age of Rohini and Keerthi after 4 years:
- Rohini: 16 + 4 = 20
- Keerthi: 4 + 4 = 8
- Total: 20 + 8 = 28
Final Comparison
- Quantity I (29) > Quantity II (28)
Conclusion
- The correct answer is option 'A': Quantity I > Quantity II.