Question

4. The average of four consecutive odd numbers
is 24. Find the largest number
(A) 25
(B) 27
(C) 29
(D) 31​

Answer 1

Answer:

21+23+25+27 = 96

96/4 = 24 as total observation/no.of observation= average of the numbers

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Answer 2

Given :-

The average of four consecutive odd numbers  is 24.

To Find :-

The largest number.

Analysis :-

Consider the four odd consecutive numbers as variables.

Make an equation by substituting the values in the formula of mean average.

Then find the value of the variable.

Solution :-

Let the largest odd number be 'x'. Then the other numbers would be x-6, x-4 and x-2.

By the formula,

$\underline{\boxed{\sf Mean \ average=\dfrac{Sum \ of \ values}{Number \ of \ values} }}$

Given that,

The average of four consecutive odd numbers  is 24.

Substituting their values,

$\sf \dfrac{(x-6)(x-4)(x-2)+x}{4} =24$

$\sf =4x-12=4 \times 24$

$\sf =4x-12=96$

By transposing 12,

$\sf = 4x=96+12$

$\sf =4x=108$

Finding the value of x,

$\sf x=\dfrac{108}{8}$

$\sf x=27$

Therefore, the largest odd number is 27.