Arithmetic Aptitude 3

Let the present age of Vinod and Ashok be 3x years and 4x years respectively.

Then (3x+5) / (4x+5)  = 7 / 9 

∴ 9(3x + 5) = 7(4x + 5)
∴ 27x + 45 = 28x + 35
∴ x = 10
∴ Ashok’s present age = 4x = 40 years 

Let the present age of Ram and Shyam be 6x years and 5x years respectively.

Then 5x + 7 = 32
∴      5x = 25
∴        x = 5
∴ Present age of Ram = 6x = 30 years

Let the current ages of A, B and C be ax years, 5x years and 9x respectively.

Then (4x-9) + (5x-9) + (9x-9) =45
∴ 18x – 27 = 45
∴ 18x = 72
∴ x = 4

Present ages of A, B and C are 4x = 16, 5x = 20, 9x = 36 respectively.

Le the present ages of son and his mother are x years and 3x years.

Then (3x + 12) = 2( x + 12)
∴ 3x + 12 = 2x + 24
∴ x = 12
∴ Present age of mother = 3x = 36 years 

A – B = C – A
∴ 2A = B + C
And also given that B + C = 68
∴ 2A = 68
∴   A = 34 

Opportunistic reasoning is a method of selecting suitable logical inference strategy from the knowledge base of the AI system. Blackboard is an AI model of opportunistic reasoning where a common knowledge base is updated frequently by diverse knowledge sources. So, (B) is the correct option.