The average age of Ram and Rohan is 45 years. If Aravind were to replace Ram, the average age would be 44 years; and if Aravind were to replace Rohan, the average age would be 46 years. What are the ages of Ram, Rohan and Aravind, respectively, in years?

Correct option is D

Given:
Average age of Ram and Rohan = 45
Average age of Aravind and Rohan = 44
Average age of Ram and Aravind = 46
Formula Used:
Sum = Average × Number of Entities
Solution:
Let the ages of Ram, Rohan, and Aravind be R, r, and A respectively.
Formulate the sum equations:
R + r = 45 × 2 = 90 (Equation 1)
A + r = 44 × 2 = 88 (Equation 2)
R + A = 46 × 2 = 92 (Equation 3)
Subtract Equation 2 from Equation 1:
(R + r) - (A + r) = 90 - 88
R - A = 2 (Equation 4)
Add Equation 3 and Equation 4:
(R + A) + (R - A) = 92 + 2
2R = 94
R = 47
Substitute R = 47 into Equation 3:
47 + A = 92
A = 45
Substitute R = 47 into Equation 1:
47 + r = 90
r = 43
The ages are Ram = 47, Rohan = 43, Aravind = 45.
Final Answer
So the correct answer is (d)