Question

The sum of ages of a father and his son is 60 years. If 5 years ago the age of
the father was 4 times of his son, then their present ages are -
(a) 20 years, 40 years
(b) 15 years, 40 years
(c) 15 years, 45 years
(d) 10 years, 50 years​

Answer 1

Answer :

★ Option (c) 15 years, 45 years

• The age of father = 45 years
• The age of son = 15 years

Given :

• Sum of ages of a father and his son = 60 years
• Their ages 5 years ago :-
• The age of father was 4 times the age of his son.

To find :

• The present age of the son and his father

Solution :

Let,

• Present age of father = x
• Present age of son = y

According to the first condition given :

Age of father + Age of son = 60

• x + y = 60 -----(1)

Their ages 5 years ago :

→ Age of father = x - 5 years

→ Age of son = y - 5 years

According to the second condition given :

Age of father = 4(Age of son)

• x - 5 = 4(y - 5)

→ x - 5 = 4 × y - 4 × 5

→ x - 5 = 4y - 20

Grouping the like terms and changing their signs, by transposing :

→ x - 4y = - 20 + 5

→ x - 4y = - 15

• x - 4y = - 15

Solving (1) and (2) :

⠀⠀⠀⠀⠀⠀ x + y = 60

⠀⠀⠀⠀⠀⠀x - 4y = - 15

⠀⠀⠀⠀⠀ (-) (+) ⠀⠀(+)

⠀⠀⠀⠀ _____________

⠀⠀⠀⠀⠀⠀⠀⠀5y = 75

⠀⠀⠀⠀ ______________

→ 5y = 75

Transposing 5 to the right hand side :

→ y = 75 ÷ 5

→ y = 15

The value of y = 15

Substitute the value of x in (1)

→ x + y = 60

→ x + 15 = 60

→ x = 60 - 15

→ x = 45

The value of x = 45

Substituting the value of x and y in the ages :

• The age of father = x = 45 years
• The age of son = y = 15 years

━━━━━━━━━━━━━━━━━━━━━━━

VERIFICATION :

To verify the value the age of the father and his son, add both the ages if they sum upto 60 (as mentioned in the question) then the values are right.

→ Age of father + Age of son

→ 45 + 15

→ 60

Age of father + age of son = 60

Hence, verified.

Answer 2

Answer:

(c) 15 years, 45 years

Explanation

Let the present age of son be x.

Then, present age of father is (60−x).

• According to the question,

$\sf⇒ (60−x)−5=4(x−5) \\ \\ \\ \sf⇒ 55−x=4x−20 \\ \\ \\ \sf⇒ 55+20=4x+x \\ \\ \\ \sf⇒ 75=5x \\ \\ \\ \sf⇒ x= \cancel \frac{75}{5} \\ \\ \\ \sf⇒ x=15$

∴ Son's age after 5 years = x =15 years

∴ Father's age after 5 years = (60-x) years

=(60-15)years

=45 years

$\sf \: Hence, \: The \: son's \: age \: is \: \bold{15 \: years} \: and \: Father's \: age \: is \: \bold{ 45 \: years.}$

$\rule{300px}{.7ex}$