Let the ages of father and son 10 years ago be 3$ x $ and $ x $ years respectively.
Then, $\left(3x + 10\right)$ + 10 = 2[$\left( x + 10\right)$ + 10]
$\Rightarrow$ 3$ x $ + 20 = 2$ x $ + 40
$\Rightarrow x $ = 20.
$\therefore$ Required ratio = $\left(3x + 10\right)$ : $\left(x + 10\right)$ = 70 : 30 = 7 : 3.
Ratio of the present age of Kiran and Syam = 5 : 4
Let the present age of Kiran = 5$x$
Present age of Syam = 4$x$
After 3 years, ratio of their ages = 11:9
=> $\left(5x + 3\right)$ : $\left(4x + 3\right)$ = 11 : 9
=> 9$\left(5x + 3\right)$ = 11$\left(4x + 3\right)$
=> 45$x$ + 27 = 44$x$ + 33
=> $x$ = 33-27 =6
Syams present age = 4$x$ = $(4 \times 6)$ = 24
Let the age before 10 years = $x$
Then $\dfrac{125x}{100}$ = $x$ + 10
=>125$x$ = 100$x$ + 1000
=> $x$ = $\dfrac{1000}{25}$= 40
Present age = $x$ + 10 = 40 +10 = 50
Let Rahuls age be $ x $ years.
Then, Sachins age = $\left(x - 7\right)$ years.
| $\therefore \dfrac{x - 7}{x} $=$ \dfrac{7}{9} $ |
$\Rightarrow$ 9$ x $ - 63 = 7$ x $
$\Rightarrow$ 2$ x $ = 63
$\Rightarrow x $ = 31.5
Hence, Sachins age =$\left(x - 7\right)$ = 24.5 years.
Let Cs age be $ x $ years. Then, Bs age = 2$ x $ years. As age = $\left(2x + 2\right)$ years.
$\therefore$ $\left(2x + 2\right)$ + 2$ x $ + $ x $ = 27
$\Rightarrow$ 5$ x $ = 25
$\Rightarrow x $ = 5.
Hence, Bs age = 2$ x $ = 10 years.
Let John’s present age be x
John’s age before 5 years = (x - 5)
John’s age after 10 years = (x + 10)
We are given that, John’s age after 10 years (x + 10) is 5 times his age 5 years back (x – 5)
Therefore,
(x + 10) = 5 (x – 5)
Solving the equation, we get
x + 10 = 5x – 25
4x = 35
x = 8.75 years
Let the daughter's age be x and father's age be 4x.
So as per question, 4x + 5 = 3(x + 5). So x = 10.
Hence present age of daughter is 10 years and present age of father is 40 years.
So after 5 + 5 = 10 years, daughter age would be 20 years and father’s age would be 50 years.
Hence father would be 50/20 = 2.5 times of daughter’s age.
Let Aman's present age be x
Aman's age before 10 years = x - 10)
Aman's age after 20 years = (x + 20)
We are given that, Aman's age after 20 years (x + 20) is 10 times his age 10 years back (x – 10)
Therefore, (x + 20) = 10 (x – 10)
Solving the equation, we get x + 20 = 10x – 100
9x = 120, x = 13.3 years
Let age of Romi be y
Nisha is 15 years elder than Romi = (y + 15). So Nisha's age 5 years ago = (y + 15 – 5).
Romi's age before 5 years = (y – 5)
5 years ago, Nisha is 3 times as old as Romi
(y + 15 – 5) = 3 (y – 5)
(y + 10) = (3y – 15)
2y = 25 ⇒ y = 12.5v
Romi's age = 12.5 yearsv
Nisha's age = (y + 15) = (12.5 + 15) = 27.5 years.
We are given that age ratio of Honey: Piyush = 2: 3
Honey’s age = 2x and Piyush’s age = 3x
One year ago, their age was 2x and 3x.
Hence at present, Honey's age = 2x +1 and Piyush's age = 3x +1
After 5 years, Honey’s age = (2x +1) + 5 = (2x + 6)
Piyush's age = (3x +1) + 5 = (3x + 6)
After 5 years, this ratio becomes 4: 5.
Therefore,
(2x+6) / (3x+6) = 4/5
10x + 30 = 12x + 24 ⇒ x = 3
Piyush's present age = (3x + 1) = (3x 3 + 1) = 10 years
Honey's present age = (2x + 1) = (2x 3 + 1) = 7 years