Let their present ages be 4x, 7x and 9x years respectively.

Then, (4x - 8) + (7x - 8) + (9x - 8) = 56

 20x = 80

 x = 4.

So , Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

Mother's age when Ayesha's brother was born = 36 years.

Father's age when Ayesha's brother was born = (38 + 4) years = 42 years.

Therefore  Required difference = (42 - 36) years = 6 years.

Let the mother's present age be x years.

Then, the person's present age = \(\left(\frac{2}{5}x\right) years.\)

Therefore  \(\left(\frac{2}{5}x+8\right) = \frac{1}{2}(x+8)\)

 2(2x + 40) = 5(x + 8)

 x = 40.

Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R - Q = ?.
Explanation:
R - Q = Q - T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R - Q) = ?
Here we know the value(age) of Q (25), but we don't know the age of R.
Therefore, (R-Q) cannot be determined.

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

 3x + 20 = 2x + 40

 x = 20.

So,  Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

 -  Let Kumar’s present age be x years and Selva’s present age be y years
Then, according to the first condition,
x - 10 = 3(y - 10)
or, x – 3y = -20                      ……..(1)
Now. Kumar's age after 10 years  = (x + 10) years
Selva's age after 10 years = (y + 10)
(x+10) = 2(y+10)
or, x – 2y = 10                       ……..(2)
Solving (1) and (2), we get
x = 70 and y = 30
Kumar's age = 70 years and Selva's age = 30 years.

Let Kumar's present age be denoted by K, and Selva's present age be denoted by S.

Ten years ago, Kumar's age was K-10, and Selva's age was S-10.

According to the first condition, ten years ago Kumar was thrice as old as Selva was:

K-10 = 3(S-10)

Expanding the brackets and simplifying, we get:

K-10 = 3S-30

K = 3S-20 --(1)

According to the second condition, ten years hence Kumar will be twice as old as Selva will be:

K+10 = 2(S+10)

Expanding the brackets and simplifying, we get:

K+10 = 2S+20

K = 2S+10 --(2)

We can now solve equations (1) and (2) simultaneously to find the values of K and S.

Substituting equation (1) into equation (2) for K, we get:

3S-20 = 2S+10

Solving for S, we get:

S = 30

Substituting this value of S into equation (1) for K, we get:

K = 3S-20 = 90-20 = 70

Therefore, Kumar's present age is 30 (Option A).

To summarize the solution process, we used the following steps:

• Defined variables for Kumar's and Selva's present ages (K and S).
• Used the given information to write two equations relating K and S.
• Solved these equations simultaneously to find K and S.
• Checked the solution by ensuring that it satisfies both of the original conditions.

If you think the solution is wrong then please provide your own solution below in the comments section .