Question

The sum of present ages of a father and his son is 70 years. If after 10years the ratio of their ages will be 2:1, and then what is the present age of the son ?

Answer 1

$\huge \boxed{ \underline{ \underline{ \bf{Answer}}}}$


Let the present age of father and son be
'x' and 'y' years respectively.


A/Q,

$\bf{Equation \: 1} :$

$= > \: x + y = 70 \:$

$= > \: x = 70 - y \: \: \: \: \: - - - > (equation \: 1)$

$\bf{Equation \: 2} :$

$= > \: \frac{x + 10}{y + 10} = \frac{2}{1}$

$= > \: \frac{(70 - y) + 10}{y + 10} = \frac{2}{1} \: \: \: \: \: \: \: (from \: {equ}^{n} .1)$

$= > \: \frac{80 - y}{y + 10} = 2$

$= > \: 80 - y = 2y - 20$

$= > \: 3y \: = \: 80 + 20$

$= > 3y = 60$

$= > \: y = 20$


Now , putting the y=20 in equation (1) we get,

$= > \: x \: = 70 - 20$

$= > \: x \: = \: 50$


So, Present age of

$\boxed{ \bf{Father \: = 50 \: years \: }} \: and$

$\boxed{ \bf{Son \: = \: 20 \: years}}$

Answer 2

Let Present Age of Father=X years

Let Present Age of Son=Y years

Their ages Sum=70 years

Means

Father Present Age +Son Present Age=70

X+Y=70

X=70-Y

After 10 Years

Father Age will be=(X+10) Years

Son Age will be=(Y+10) Years

Ratio Of Their Age will be=2:1

So,

$\frac{x + 10}{y + 10} = \frac{2}{1} \\ \\ x + 10 = 2(y + 10) \\ \\ x + 10 = 2y + 20$

x=70-y

$70 - y + 10 = 2y + 20 \\ \\ 80 - y = 2y + 20 \\ \\ - y - 2y = 20 - 80 \\ \\ - 3y = - 60 \\ \\ y = \frac{ - 60}{ - 3} \\ \\ y = 20$

We know X=70-Y

X=70-20

X=50 years

Present Age of Son=x=20 years

Present Age of Father=y=50 years

$\underline{Another \:Method}$

After 10 years Age will be in Ratio 2:1 Means Father Age will be 2 Times The son

Equation Can be Set

2(son age after 10 years)=Father Age after 10 years

2(y+10)=X+10

2y+20=70-y+10

2y+20=80-y

2y+y=80-20

3y=60

y=60/3

y=20

Y=20

X=70-y

x=70-20

X=50

Son Present Age=20 years

Father Present Age=50 years