Question

The arithmetic mean of $5$ numbers is $27$.

If one of the numbers be excluded then their mean is $25$

The excluded number is?

• A. $28$
• B. $26$
• C. $25$
• D. $35$

Answer 1

The correct option is D $35$

Mean is the sum of the numbers divided by the total number of values.

Given that the arithmetic mean of $5$ numbers is $27$.

Let the numbers be $x_1,x_2,x_3,x_4,x_5$

Therefore, $27=\frac{x_1+x_2+x_3+x_4+x_5}{5}$

$x_1+x_2+x_3+x_4+x_5=27\times 5=135$ -------(1)

After excluding one number then the mean is $25$

Let the excluded number be $x_5$

Therefore, $25=\frac{x_1+x_2+x_3+x_4}{4}$

$x_1+x_2+x_3+x_4=25\times 4=100$ ------(2)

subtracting (1) and (2) we get

$(x_1+x_2+x_3+x_4+x_5)-(x_1+x_2+x_3+x_4)=135-100$

$⟹x_5=35$

Therefore, the excluded number is $35$