Question
The current ages of 'Aman' and 'Bhanu' are in the ratio
2:5, respectively. 'y' years ago, the age of 'Bhanu' was twice the age of 'Chinky,' while 'y' years from now, the age of 'Bhanu' will be twice the age of 'Aman.' If the difference between the present ages of 'Aman' and 'Chinky' is even and is the cube of a prime number, then determine the sum of the present ages of 'Aman' and 'Chinky.'Solution
We can say that present ages of 'Aman' and 'Bhanu' be '2a' years and '5a' years, respectively Let present age of 'Chinky' be 'c' years ATQ; (5a + y) = 2 × (2a + y) Or, 5a + y = 4a + 2y Or, y = a Also, (5a - y) = 2 × (c - y) Or, 5a - a = 2c - 2a Or, c = 3a Since, '2' is the only prime number whose cube is even So, difference between present ages of 'Aman' and 'Chinky' = 8 years So, 3a - 2a = 8 Or, a = 8 So, sum of present age of 'Aman' and 'Chinky' = 2a + 3a = 5a = 5 × 8 = 40 years
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