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

$\bf{\huge{\underline{\boxed{\rm{\pink{Answer:}}}}}}$

Given :-

• 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.

To find :-

• Present age of Man
• Present age of Son.

Sóĺúťíóń :-

Let the present age of Man be x years.

Let the present age of son be y years.

As per the first condition :-

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

Ages 5 years ago :-

Man = x - 5 years

Son = y - 5 years

Man was seven times old as son

Let's represent it mathematically to get our equation,

x - 5 = 7 ( y - 5)

x - 5 = 7y - 35

x - 7y = - 35 + 5

x - 7y = - 30 -----> 1

As per the second condition :-

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

Ages 5 years hence :-

Man = x + 5 years

Son = y + 5 years

Father will be three times as old as his son.

Let's represent it mathematically to get our second equation,

x + 5 = 3 ( y + 5)

x + 5 = 3y + 15

x - 3y = 15 - 5

x - 3y = 10 -----> 2

Solve equations 1 and 2 simultaneously by elimination method.

Subtracting equation 2 from 1,

..+ x - 7y = - 30 ----> 1

-(+ x - 3y = +10 ) ---> 2

---------------------------------

- 4y = - 40

4y = 40

y = $\bf\frac{40}{4}$

y = 10

Substitute y = 10 in equation 1,

x - 7y = - 30 ----> 1

x - 7 (10) = - 30

x - 70 = - 30

x = - 30 + 70

x = 40

•°• Present age of Man = x = 40 years

Present age of Son = y = 10 years

$\bf{\huge{\underline{\boxed{\rm{\purple{Verification:}}}}}}$

For first case :-

• Present age of Man = 40 years
• Present age of son = 10 yesrs

Ages 5 years ago :-

Man = 40 - 5 = 35 years = x

Son = 10 - 5 = 5 years = y

Man was seven times as old as his son.

x = 7(y)

35 = 7 (5)

35 = 35

LHS = RHS.

For second case :-

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

Ages five years ago :-

Man = 40 + 5 = 45 years = x

Son = 10 + 5 = 15 years = y

Father will be three times as old as his son.

x = 3 (y)

45 = 3 (15)

45 = 45

LHS = RHS.

Hence verified.

Answer 2

$\huge\sf{Answer:-}$

Let y be the age of son.

Let 7y be the age of father.

y + 5 , 7y + 5 are the present ages

= y + 10 future age of son.

7y + 10 is father.

= (7y + 10 = 3) (y + 10)

= (y = 5)

= (7y = 35)

(y + 5 = 5 + 5 = 10)

.•. 10 years is age of son and

(7y + 5 = 7) ×( 5 + 5 = 40) .•. 40 is age of father.

Hope it helps!