Question

10 years ago father was 12 time as old as his son and 10 years hence, he will be twice as old as his son. find their present age
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Answer 1

Step-by-step explanation:

Given :-

10 years ago father was 12 time as old as his son.

10 years hence, he will be twice as old as his son.

To find :-

The present ages of father and son .

Solution :-

Let the present age of son be X years

Let the present age of father be Y years

10 years ago his age = (X-10) years

10 years ago his father age = (Y-10) years

According to the given problem

10 years ago father was 12 time as old as his son

10 years ago

=> Father's age = 12×son's age

=> (Y-10) = 12 (X-10)

=> Y - 10 = 12X-120

=> Y = 12X-120+10

=> Y = 12X-110 -----------------(1)

After 10 years son's age = (X+10) years

After 10 years his father's age

= (Y+10) years

According to the given problem

10 years hence, he will be twice as old as his son

=> Father's age = 2×Son's age

=> Y+10 = 2(X+10)

=> Y +10 = 2X+20

=> Y = 2X+20-10

=> Y = 2X+10 -----------------(2)

From (1)&(2)

12X-110 = 2X+10

=> 12X-2X = 10+110

=> 10X = 120

=> X = 120/10

=> X = 12 years

On substituting the value of X in (2) then

Y = 2(12)+10

=> Y = 24+10

=> Y = 34 years

Therefore, X = 12 years and Y = 34 years

Answer :-

Present age of father = 34 years

Present age of son = 12 years

Check :-

Present age of father = 34 years

Present age of son = 12 years

10 years ago their ages

Father's age = 34-10 = 24 years and

Son's age = 12-10= 2 years

Father's age = 24 years

=> 2×12

=> 12× Son's age

And

After 10 years their ages will be

34+10= 44 years

and 12+10 = 22 years

Father's age = 44 = 2(22) years

=> Twice the age of son

Verified the given relations in the given problem.

Answer 2

Answer:

Given :-

• 10 years ago father age was 12 times as old as his son and 10 years hence, he will be twice as old as his son.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \sf Age_{(Son)} =\: x\: years$

$\mapsto \sf Age_{(Father)} =\: 12x\: years$

✫ Present year of son and father :

$\leadsto \bf Present\: Age_{(Son)} =\: (x + 10)\: years$

$\leadsto \bf Present\: Age_{(Father)} =\: (12x + 10)\: years$

✫ After 10 years their ages will be :

✭ Age Of Son :

$\implies \sf Age_{(Son)} =\: (x + 10 + 10)\: years$

$\implies \sf\bold{\blue{Age_{(Son)} =\: (x + 20)\: years}}$

✭ Age Of Father :

$\implies \sf Age_{(Father)} =\: (12x + 10 + 10)\: years$

$\implies \sf\bold{\blue{Age_{(Father)} =\: (12x + 20)\: years}}$

According to the question :

$\longrightarrow \bf 12x + 20 =\: 2(x + 20)$

$\longrightarrow \sf 12x + 20 =\: 2x + 40$

$\longrightarrow \sf 12x - 2x =\: 40 - 20$

$\longrightarrow \sf 10x =\: 20$

$\longrightarrow \sf x =\: \dfrac{2\cancel{0}}{1\cancel{0}}$

$\longrightarrow \sf x =\: \dfrac{2}{1}$

$\longrightarrow \sf\bold{\purple{x =\: 2\: years}}$

Hence, the required present ages are :

☆ Present Age Of Son :

$\dashrightarrow \sf Present\: Age_{(Son)} =\: (x + 10)\: years$

$\dashrightarrow \sf Present\: Age_{(Son)} =\: (2 + 10)\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(Son)} =\: 12\: years}}$

☆ Present Age Of Father :

$\dashrightarrow \sf Present\: Age_{(Father)} =\: (12x + 10)\: years$

$\dashrightarrow \sf Present\: Age_{(Father)} =\: \{12(2) + 10\}\: years$

$\dashrightarrow \sf Present\: Age_{(Father)} =\: (24 + 10)\: years$

$\dashrightarrow \sf\bold{\red{Present\: Age_{(Father)} =\: 34\: years}}$

$\therefore$ The present age of son is 12 years and the present age of father is 34 years.