# Moderate Averages Solved QuestionAptitude Discussion

 Q. Average of ten positive numbers is $x$. If each number is increased by $10\%$, then $x$ :
 ✖ A. remains unchanged ✖ B. may decrease ✖ C. may increase ✔ D. is increased by $10\%$

Solution:
Option(D) is correct

Let 10 numbers be $x_1, x_2, x_3 ….. x_{10}$

According to question average of these 10 numbers is 10.

$⇒ (x_{1} + x_{2} + x_{3} + …….. + x_{10})/10 = x$

Now if each number is increased by $10\%$, then new average, say $y$,

$y = (1.1 x_1 + 1.1 x_2 + 1.1 x_3 + ……… + 1.1 x_{10})/10$

$⇒ y = 1.1 × ((x_1 + x_2 + x_3 + …….. + x_{10})/10)$

$⇒ y= 1.1 x$

$⇒ y$ is $10\%$ increased.

Edit: A typo has been corrected ($\%$ sign has been added in the question) after it was pointed out by Zoha Amjad.

Edit 2: Another typo has been corrected after it was pointed by Sravan Reddy.

## (4) Comment(s)

Sravan Reddy
()

Another typo - you missed "is increased" word in the question :)

Deepak
()

Thank you Sravan for pointing it out. Corrected the question.