Question

Two years ago a man was five times as old as his son. Two years later his age will be 8 more than

Answer 1

Given:-

• Two years ago, a man was five times as old as his son.

• Two years later,  his age will be 8 more than three times the age of the son.

To find out:-

Find the present ages of the man and his son.

Solution:-

Let the present age of his son be a.

Then, the present age of the father = b

According to the question,

★ Two years ago,

⇒( b - 2 ) = 5 ( a - 2 )

⇒ b - 2 = 5a - 10

 

⇒ b = 5a - 8 .......( 1 )

★ Two years later,

b + 2 = 8 + 3 ( a + 2 )

⇒ b + 2 = 8 + 3a + 6

⇒ b + 2 = 3a + 14

⇒ b = 3a + 12.......( 2 )

From ( 1 ) and ( 2 )

5a - 8 = 3a + 12

⇒ 5a - 3a = 12 + 8

⇒ 2a = 20

⇒ a = 10

Now,

Substituting the value of a in equation ( 1 )

b = 5a - 8

b = 5 × 10 - 8

b = 50 - 8

b = 42

Hence,the present age of man and his son are 42 and 10 respectively.

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \pink{Question:-}}}}}}$

Two years ago a man was five times as old as his son. Two years later his age will be 8 more than..

_______________

${ \huge{ \bold{ \underline{ \underline{ \orange{Answer:-}}}}}}$

✒Given : -

• Two years ago a man was five times as old as his son ...
• After two years his age will be 8 more than 3 times of his son's age ...

✒To Find : -

• Present age of man and his son = ?

✒Let ,

• Let present age of Son be = x
• Let presebt age of man be = y

${ \large{ \bold{ \underline{ \underline{ \purple{According\:to\:the\:Question:-}}}}}}$

★ Two years ago ★

$\dashrightarrow\sf{(y-2)=5(x-2)}$

$\dashrightarrow\sf{y-2=5x-10}$

$\dashrightarrow\sf{y=5x-8}$ ➮ (1)

★ After two years ★

$\dashrightarrow\sf{y+2=8+3(x+2)}$

$\dashrightarrow\sf{y+2=8+3x+6}$

$\dashrightarrow\sf{y+2=3x+14}$

$\dashrightarrow\sf{y=3x+12}$ ➮ (2)

✒Now ,

✒By Equation : -

$\dashrightarrow\sf{5x-8=3x+12}$

$\dashrightarrow\sf{5x-3x=12+8}$

$\dashrightarrow\sf{2x=20}$

$\dashrightarrow\sf{x=\cancel\dfrac{20}{2}}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \green{x=10}}}}}}}$

✒Now ,

✒On Substituting Values of x in Eq. (1) : -

$\dashrightarrow\sf{y=5x-8}$

$\dashrightarrow\sf{y=5\times{10}-8}$

$\dashrightarrow\sf{y=50-8}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \red{y=42}}}}}}}$

Therefore , Present age of man is 42 years and Present age of his son is 10 years ..