Question

The sum of three consecutive odd numbers is 69. Find the numbers.
The sum of the ages of a father and his son is 60 years. If the son's age is
than the father's age, find the age of the father.

Answer 1

Question:-

The sum of three consecutive odd numbers is 69. Find the numbers.

Solution:-

Let the three consecutive odd numbers be M, M +2 and M + 4.

Sum of three consecutive odd numbers is 69.

According to question,

⇒ M + M + 2 + M + 4 = 69

⇒ 3M + 6 = 69

⇒ 3M = 69 - 6

⇒ 3M = 63

⇒ M = 63/3

⇒ M = 21

Therefore,

First number = M

⇒ 21

Second number = M + 2

⇒ 21 + 2

⇒ 23

Third number = M + 4

⇒ 21 + 4

⇒ 25

•°• Three consecutive odd numbers are 21, 23 and 25.

$\rule{200}2$

Correct Question:-

The sum of the ages of a father and his son is 60 years. 5 years ago, age of father was four times the age of son, find the age of the father and son.

Solution:-

Let the age of father be x years and his son be y years.

Sum of ages of father and his son is 60 years.

According to question,

⇒ x + y = 60

⇒ x = 60 - y

5 years ago,

• age of father = (x - 5) years
• age of son = (y - 5) years

According to question,

⇒ x - 5 = 4(y - 5)

⇒ x - 5 = 4y - 20

Substitute the value of x in above equation

⇒ 60 - y - 5 = 4y - 20

⇒ 55 - y = 4y - 20

⇒ 55 + 20 = 4y + y

⇒ 75 = 5y

⇒ y = 15

Now, substitute value of y in x

⇒ x = 60 - 15

⇒ x = 45

•°• Present age of father is 45 years and son is 15 years.

Answer 2

Question (1) :----- The sum of three consecutive odd numbers is 69. Find the numbers. ?

Solution :---

Let the First odd number be = x .

Than,

→ Second consecutive odd number = (x +2).

→ Third consecutive ord number = (x+2) + 2 = (x+4).

Now, it is given that, sum of all three is 69.

A/q,

→ x + (x+2) + (x+4) = 69

→ 3x + 6 = 69

→ 3x = 63

Dividing both sides by 3 ,

→ x = 21 ..

So, First odd number = x = 21.

→ Second consecutive odd number = (x +2) = 21+2 = 23

→ Third consecutive ord number = (x+4) = 21+4 = 25 .

Hence, Three consecutive odd Numbers whose sum will be 69 are 21, 23 and 25..

_______________________

✪✪ Shortcut✪✪ :-----

As we know that, Average is the Middle value of Numbers.

Given, Sum of 3 consecutive odd numbers = 69 .

→ Average = Sum of observation / Number of observation.

→ Average = 69/3 = 23.

So, we can say that 23 is our Middle odd Number out of three .

So,

→ First odd Number = 23 - 2 = 21

→ Third odd Number = 23 +2 = 25..

Hence, Three consecutive odd Numbers whose sum will be 69 are 21, 23 and 25..

______________________________

Question (2) :-- The sum of the current ages of a father and his son is 60 years. Five years ago, the father's age was four times the age of the son. Find present age of Father and son .. ?

Solution :---

Let Son Present age = x years.

→ Father Present age = (60-x) years.

Now,

→ 5 years ago , son was = (x-5) years old.

→ 5 yrs ago, Father was = (60-x) - 5 = (55-x) years old..

It is given that, Father was Four times the age of the son.

A/q,

→ 4(x-5) = (55-x)

→ 4x - 20 = 55 - x

→ 4x + x = 55 + 20

→ 5x = 75

Dividing both sides by 5 ,

→ x = 15

So,

→Son Present age = x = 15 years.

→ Father Present age = (60-x) = 60-15 = 45 years.

Hence, Now, son is 15 years old and his Father is 45 years old...