Averages
Aptitude

 Back to Questions
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 $10\%$

 Hide Ans

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.


Zoha Amjad
 ()

the question is incomplete


Deepak
 ()

Thank you Zoha, corrected the typo.