Let the ages of children be $ x $, $\left( x + 3\right)$, $\left(x + 6\right)$, $\left(x + 9\right)$ and $\left(x + 12\right)$ years.
Then, $ x $ + $\left(x + 3\right)$ + $\left(x + 6\right)$ + $\left(x + 9\right)$ + $\left(x + 12\right)$ = 50
$\Rightarrow$ 5$ x $ = 20
$\Rightarrow x $ = 4.
$\therefore$ Age of the youngest child = $ x $ = 4 years.
Let my age = $x$
Then
My brothers age = $x$ + 3
My mothers age = $x$ + 26
My sisters age = $\left(x + 3\right)$ + 4 = $x$ + 7
My fathers age = $\left(x + 7\right)$ + 28 = $x$ + 35
=> age my father when my brother was born = $x$ + 35 - $\left(x + 3\right)$ = 32
Let the present age of the man and his wife be 4$x$ and 3$x$ respectively.
After 4 years this ratio will become 9 : 7
=> $\left(4x + 4\right)$ : $\left(3x + 4\right)$ = 9 : 7
=> 7$\left(4x + 4\right)$ = 9$\left(3x + 4\right)$
=> 28$x$ + 28 = 27$x$ + 36
=> $x$ = 8
Present age of the man = 4$x$ = 4×8 = 32
Present age of his wife = 3$x$ = 3×8 = 24
Assume that they got married before t years. Then
(32 - t) : (24 - t) = 5 : 3
3(32 - t) = 5(24 - t)
=> 96 - 3t = 120 - 5t
=> 2t = 24
=> t = $\dfrac{24}{2}$ = 12
Let Ronits present age be $ x $ years. Then, fathers present age =$\left(x+ 3x\right)$ years = 4$ x $ years.
| $\therefore$ $\left(4x+ 8\right)$ =$ \dfrac{5}{2}\left(x+ 8\right)$ |
$\Rightarrow$ 8$ x $ + 16 = 5$ x $ + 40
$\Rightarrow$ 3$ x $ = 24
$\Rightarrow x $ = 8.
| Hence, required ratio =$ \dfrac{(4x + 16)}{(x + 16)} $=$ \dfrac{48}{24} $= 2. |
Let the sons present age be $ x $ years. Then, mans present age = $\left(x + 24\right)$ years.
$\therefore$ $\left(x + 24\right)$ + 2 = 2$\left(x + 2\right)$
$\Rightarrow x $ + 26 = 2$ x $ + 4
$\Rightarrow x $ = 22.
Mothers age when Ayeshas brother was born = 36 years.
Fathers age when Ayeshas brother was born = (38 + 4) years = 42 years.
$\therefore$ Required difference = (42 - 36) years = 6 years.
Let the sons present age be $ x $ years. Then,$\left (38 - x\right)$ = $ x $
$\Rightarrow$ 2$ x $ = 38.
$\Rightarrow x $ = 19.
$\therefore$ Sons age 5 years back (19 - 5) = 14 years.
Let the present ages of Sameer and Anand be 5$ x $ years and 4$ x $ years respectively.
| Then,$ \dfrac{5x + 3}{4x + 3} $=$ \dfrac{11}{9} $ |
$\Rightarrow$ 9$\left(5x+ 3\right)$ = 11$\left(4x+ 3\right)$
$\Rightarrow$ 45$ x $ + 27 = 44$ x $ + 33
$\Rightarrow$ 45$ x $ - 44$ x $ = 33 - 27
$\Rightarrow x $ = 6.
$\therefore$ Anands present age = 4$ x $ = 24 years.
Let the age of the son before 8 years = $x$
Then age of Kamal before 8 years ago = 4$x$
After 8 years, Kamal will be twice as old as his son
=> 4$x$ + 16 = 2$\left(x + 16\right)$
=> $x$ = 8
Present age of Kamal = 4$x$ + 8 = 4×8 + 8 = 40
Present age of Denis = 5 years
Present age of Rahul = 5 - 2 = 3
Let the present age of Ajay = $x$
Then $\dfrac{x-6}{18}$ = present age of Rahul = 3
=> $x$ - 6 = 3×18 = 54
=> $x$ = 54 + 6= 60