Question : If the average of three consecutive odd numbers is 23, then which is the greatest among these odd numbers?
Correct Answer 25
Solution & Explanation
Explanation
Given, the average of three consecutive odd numbers = 23
Before solving the question, it is necessary to see some important terms, such as consecutive numbers, consecutive odd numbers, etc. used in this question.
Consecutive Numbers
Numbers in the continuation are called Consecutive Numbers, for example, 1, 2, 3, 4, . . . etc.
Odd Numbers
Numbers which cannot be divided exactly by 2, are called Odd Numbers, for example, 1, 3, 5, 7, 9, . . . . etc.
Consecutive Odd Numbers
Odd numbers in the continuation are called Consecutive Odd Numbers, such as 1, 3, 5, 7, . . . . etc.
How to get next consecutive odd numbers to the given odd number
Here, it can be observed easily, that there is a difference of 2 between two consecutive numbers. This means, the next consecutive odd number can be obtained by addition of 2 in an odd number.
Example:
If 1 is the first odd number, then second consecutive odd number to 1
= 1 + 2 = 3
Similarly, the third consecutive odd number to 1
= 1 + 2 + 2 = 1 + 4 = 5
And, the fourth consecutive odd number to 1
= 1 + 2 + 2 + 2 = 1 + 6 = 7 and so on.
In short, next consecutive number can be obtained by adding 2 in an odd number.
Solution of the Question
Let, the first odd number = x है।
Therefore, the second consecutive odd number = x + 2
And, the third consecutive odd number = x + 4
Formula to find the
Average = Sum of observations/Numbers of observations
Now, as per question,
The average of given consecutive odd numbers
= Sum of given consecutive odd numbers/Numbers of given odd numbers
⇒ 23 = x + (x+2) + (x+4)/3
⇒ x + (x+2) + (x+4)/3 = 23
⇒ x + x + 2 + x + 4/3 = 23
⇒ 3x + 6/3 = 23
By taking 3 as common in the above expression
⇒ 3 (x + 2)/ 3 = 23
⇒ x + 2 = 23
By transposing 2 to RHS
⇒ x = 23 – 2
⇒ x = 21
Therefore, first odd number = x = 21
Thus, second consecutive odd number = x + 2
After substituting the value of x = 21
= 21 + 2 = 23
Thus, The second consecutive odd number = 23
Similarly, the third consecutive odd number = x + 4
= 21 + 4 = 25
Therefore, the greatest among the given odd numbers = 25 Answer
Similar Questions
(1) Find the average of the first 3048 odd numbers.
(2) Find the average of the first 2064 even numbers.
(3) Find the average of the first 2121 even numbers.
(4) Find the average of the first 1451 odd numbers.
(5) Find the average of the first 2587 even numbers.
(6) What is the average of the first 1529 even numbers?
(7) Find the average of the first 2414 odd numbers.
(8) Find the average of odd numbers from 11 to 1127
(9) Find the average of the first 2870 even numbers.
(10) Find the average of odd numbers from 11 to 891