Let the present ages of Arun and Deepak be 4$ x $ years and 3$ x $ years respectively. Then,

4$ x $ + 6 = 26    $\Leftrightarrow$    4$ x $ = 20

$ x $ = 5.

$\therefore$ Deepaks age = 3$ x $ = 15 years.

Let the ages of Kunal and Sagar 6 years ago be 6$ x $ and 5$ x $ years respectively.

$\Rightarrow$ 10$\left(6x + 10\right)$ = 11$\left(5x + 10\right)$

$\Rightarrow$ 5$ x $ = 10

$\Rightarrow x $ = 2.

$\therefore$ Sagars present age = $\left(5x + 6\right)$ = 16 years.

Let the present age of P and Q be 3x and 4x respectively.

Ten years ago, P was half of Qs age

=> $\left(3x - 10\right)$ = $\dfrac{1}{2}(4x - 10)$

=> 6x - 20 = 4x - 10

=> 2x = 10

=> x = 5

total of their present ages = 3x + 4x = 7x = 7 × 5 = 35

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

Then, $\left(4x- 8\right)$ + $\left(7x - 8\right)$ + $\left(9x- 8\right)$ = 56

$\Rightarrow$ 20$ x $ = 80

$\Rightarrow x $ = 4.

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

Let the present ages of son and father be $ x $ and $\left(60 -x\right)$ years respectively.

Then,$\left (60 - x\right)$ - 6 = 5$\left(x- 6\right)$

$\Rightarrow$ 54 - $ x $ = 5$ x $ - 30

$\Rightarrow$ 6$ x $ = 84

$\Rightarrow x $ = 14.

$\therefore$ Sons age after 6 years = $\left(x+ 6\right)$ = 20 years..

Let the mothers present age be $ x $ years.

$\Rightarrow$ 2$\left(2x + 40\right)$ = 5$\left(x+ 8\right)$

$\Rightarrow x $ = 40.

Let the present age the son = $x$

Then present age of the father = 3$x$ + 3

Given that ,three years hence, fathers age will be 10 years more than twice the age of the son

=> $\left(3x + 3 + 3\right)$ = 2$\left(x + 3\right)$ +10

=> $x$ = 10

Fathers present age = 3$x$ + 3 = 3×10 + 3 = 33

Consider Ayishas present age = $x$

Then her fathers age = 6$x$

Given that Ayisha s fathers age will be twice the age of Shankars age after 10 years

=> Shankars age after 10 years =$\dfrac{1}{2}(6x + 10) = 3x + 5$

Also given that Shankars eight birthdays was celebrated two years before.

=> Shankars age after 10 years = 8 + 12 = 20

=> $3x+5=20$

=> $x=\dfrac{15}{3}=5$

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.

Explanation:

R - Q = Q - T

(R + T) = 2Q