Let the present age of the father and son be x years and (45 - x)years respectively.
Then, (x - 5)(45 - x - 5) = 4(x - 5)

Correct Option: B

Let the present age of the father and son be x years and (45 - x)years respectively.
Then, (x - 5)(45 - x - 5) = 4(x - 5)
⇒ -x² + 41x - 180 = 0
⇒ (x - 5)(x - 36) = 0
⇒ x = 36
∴ The present ages of father and son are 36 years and 9 years respectively.

Let Ramesh's present age be x years. Then Shyam's present age = 3x years.
∴ 2(x + 12) = (3x + 12)

Correct Option: C

Let Ramesh's present age be x years. Then Shyam's present age = 3x years.
∴ 2(x + 12) = (3x + 12)
⇒ x = 12
Hence, Shyam's present age is 36 years.

Let the present ages of B and A be x years and (x + 9) years respectively.
Then, (x + 9 + 10) = 2(x - 10)

Correct Option: C

Let the present ages of B and A be x years and (x + 9) years respectively.
Then, (x + 9 + 10) = 2(x - 10)
∴ x = 39

Let the present ages of son and father be x years and (56 - x) years respectively.
Then, (56 - x + 4) = 3(x + 4)

Correct Option: A

Let the present ages of son and father be x years and (56 - x) years respectively.
Then, (56 - x + 4) = 3(x + 4)
⇒ 4x = 48
⇒ x = 12
So, their present ages are 12 years, 44 years respectively.

Let A's age 10 years ago = x years
Then, B's age 10 years ago = 2x years
∵ (x + 10) / (2x + 10) = 3 / 4

Correct Option: C

Let A's age 10 years ago = x years
Then, B's age 10 years ago = 2x years
∵ (x + 10) / (2x + 10) = 3 / 4
⇒ 4(x + 10) = 3(2x + 10)
⇒ x(6 - 4) = 40 - 30
⇒ x = 5

&ther4; Total of their present ages = (x + 10) + (2x + 10)
= (3x + 20)
= 35 years