Explanation: 

Let 4 years ago A’s age = 5x, B’s age = 9x

Then 4+8 = 12 years after – (5x+12)/(9x+12) = 2/3

Solve, x = 4

B’s present age = 9x+4 = 40

Explanation: 

Let B’s age 8 yrs ago = x, then A’s age = 4x

After (8+8) = 16 years:

(4x+16) = 2 * (x+8)

Solve, x = 8

A’s present age = 4x+8 = 40

B’s present age = x+8 = 16

Explanation: 

Let A’s present age = x, Then B’s present age = 2x

After 4 years, (2x+4) = 2(x+4) – 4

0 = 0

Explanation: 

Let 10 years ago, A’s age = x, B’s age = 5x

After (10+6) = 16 years, (x+16) = (3/7) (5x+16)

Solve, x = 8

So A’s present age = x+10 = 18

Explanation: 

Let C’s present age = x, then B’s = 2x, and A’s = 2x+2

Given: x+2x+(2x+2) = 27

Solve, x = 5

A’s present age = 2x+2 = 12

C’s present age = x = 5

6 years after A+C)’s age = 12+5+6+6 = 29

Explanation: 

The difference between B and C’s age will remain same

Let C’s present age = x, so B’s present age = (x+2)

sum of the present ages of A and B is 50, so A’s age becomes = 50-(x+2) =48-x

now A is younger than C by 4 years, so 48-x = x – 4

Solve, x = 26

B’s present age = x+2 = 28

Before 8 years, B’s age = 28-8 = 20

Explanation: 

Let C’s present age = x, then A’s present age = 6x

Let B’s present age is y.

Then after 10 years, (6x+10) = 2 (y+10)

Solve, y = 3x-5 = B’s present age

B’s eighth birthday was celebrated 2 years ago, so B’s present age = 10, and also 3x-5 = 10

Solve, x = 5

Explanation: 

Let A’s present age = 5x, and B’s = 3x

Ratio of A’s age 4 years ago to B’s age 4 years hence is 1 : 1. So

(5x-4)/(3x+4) = 1/1

Solve x = 4

So A’s present age = 20, and B’s = 12

Required ratio = (20+4) : (12-4)

Let present age of son = x, then of father = x+3x = 4x

After 8 years, (4x+8) = (5/2) (x+8)

Solve, x = 8

Required ratio = (4x+16) : (x+16) = 2 : 1

Explanation: 

Let (B+C)’s present age= x

Then A’s present age = 3x

After 5 years, (3x+5) = 2*(x+5+5)

Solve, x = 15

Sum = x+3x = 4x = 60