Two years hence, the ratio of the ages of ‘B’ and

Solution

Let the ages of ‘B’ and ‘C’ two years hence from now be ‘5k’ years and ‘4k’ years respectively. Present age of ‘B’ = (5k − 2) years Present age of ‘C’ = (4k − 2) years So, present age of ‘A’ = 2 × (4k − 2) − (5k − 2) = (3k − 2) years Now, (3k − 2 − 3) × (4k − 2 − 3) = 77 Or, (3k − 5) × (4k − 5) = 77 Or, 12k² − 15k − 20k + 25 = 77 Or, 12k² − 35k − 52 = 0 Or, (12k + 13)(k − 4) = 0 So, ‘k’ = −(13/12) or ‘k’ = 4 But ‘k’ cannot be negative. So, ‘k’ = 4 Therefore, ‘p’ = (5k − 2) + 8 = 5k + 6 = 26 Statement I 26 is not a perfect square.
So, statement I is false. Statement II 26 − 2 = 24, which is not prime.
So, statement II is false. Statement III 26 + 3 = 29, which is not completely divisible by 6.
So, statement III is false. Statement IV 26 + 5 = 31 > 28.
So, statement IV is true. Therefore, one among the four statements given is true. Hence, option E.