Question

Five years ago a man was seven times as old as his son. Five years hence, the father will be

three times as old as his son. Find their present ages.​

Answer 1

To Find :

• we need to find the present age of son and his father.

Solution :

$\underline{ \underline \green{ \boldsymbol{ \dag \: According \: To \: Question : - }}}$

Five years ago a man was seven times as old as his son.

Five years ago : --

• Let the age of son be x years
• Age of father = 7x

So ,

• present age of son = x + 5
• present age of father = 7x + 5

Five years hence, the father will be three times as old as his son.

After 5 year's : --

• Age of son = x + 5 + 5 = x + 10
• Age of father = 7x + 10

But age of father is 3 times age of son .

So,

↛ 7x + 10 = 3(x + 10)

↛ 7x + 10 = 3x + 30

↛ 7x - 3x = 30 - 10

↛ 4x = 20

• ›› x = 5

So,

• Present age of father : -

= 7x + 5

= 7 × 5 + 5

= 35 + 5

= 40 years.

• present age of son

= x + 5

= 5 + 5

= 10 years.

Hence,

${ \underline \pink{ \boldsymbol{ \bullet \: Present \: Age \: of \:Son = 10 year's }}}$

${ \underline \pink{ \boldsymbol{ \bullet \: Present \: Age \: of \: Father = 40 year's }}}$

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Answer 2

Answer:

Present age of man = 40

Present age of son = 10

Step-by-step explanation:

Let the present age of the man = x

let the present age of son = y

man's age five years ago = x-5

son's age five years ago = y-5

five years ago man's age was seven times his son's age. therefore the equation will be

x-5 = 7(y-5)

x-5 = 7y - 35

x-7y= -35+5

x-7y = -30 eq. 1

man's age 5 years from now = x+5

son's age 5 years from now = y+5

after 5 years the man's age will be 3 times his son's age. Therefore the equation will be

x+5 = 3(y+5)

x+5 = 3y+15

x-3y = 15-5

x-3y = 10 eq. 2

subtract eq 1 and eq 2

(x-7y) - (x-3y) = -30-10

x-7y-x+3y = -40

-4y = 40

y = -40 ÷ -4

y = 10

since son's present age = y

and y = 10

therefore son's present age= 10

Now substitute the value of y= 10 in eq 1

x-7y = -30

x - 7×10 = -30

x - 70= -30

x = -30 + 70

x = 40

Therefore man's present age= 40