Question

6. Six years later father's age will be 3 times
Sohan's age. Three years ago, he was nine times
Sohan's age. Find their present ages. .​

Answer 1

Solution :-

Let :-

Present age of father = x

Present age of Sohan = y

6 years later :-

Age of father = x + 6

Age of Sohan = y + 6

3 years ago :-

Age of father = x - 3

Age of Sohan = y - 3

According to the first condition :-

$\longrightarrow\sf x+6=3(y+6) \\\\\longrightarrow x+6 = 3y+18 \\\\\longrightarrow x-3y = 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...........................(1)$

According to the second condition :-

$\longrightarrow \sf x-3 = 9(y-3) \\\\\longrightarrow x-3 = 9y-27 \\\\\longrightarrow x-9y = -24 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...........................(2)$

Equation (1) - Equation (2) :-

$\longrightarrow \sf 6y = 36 \\\\\longrightarrow \bf y = 6$

Substitute the value of y in eq (1) :-

$\longrightarrow \sf x - 3 \times 6= 12 \\\\\longrightarrow x -18=12 \\\\\longrightarrow \bf x = 30$

Present age of father = 30 years

Present age of Sohan = 6 years

Answer 2

$\huge {\pink {\mathtt {Given : }}}$

• Six years later father's age will be 3 times Sohan's age.
• Three years ago, he was nine times Sohan's age.

$\huge {\blue {\mathtt {To \: Find : }}}$

• Their present ages .

$\huge {\red {\mathtt {Solution : }}}$

Let the present age of sohan be " x " and his father's age be " y ".

6 years later ,

Sohan's age = x + 6

His father's age = y +6

we know that ,

Six years later father's age will be 3 times Sohan's age

so ,

y + 6 = 3 ( x+6 )

y + 6 = 3x + 18

y = 3x + 12

3 Years ago ,

Sohan's age = x -3

his father's age = y - 3

y - 3 = 9(x-3)

y -3 = 9x - 27

9x - y = 24

Subsitute the value of y in the equation 9x - y = 24

9x - (3x + 12) = 24

9x - 3x - 12 = 24

6x = 36

x = 6

y = 3x + 12

y = 3(6) + 12

y = 18 + 12 = 30

so present age of son is 6 and that of father's is 30 .