The sum of three consecutive odd numbers is 69. Find the numbers.
Answers
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..
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✪✪ 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..
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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...
Step-by-step explanation:
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.