Aptitude 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.**

**Sravan Reddy**

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

**Zoha Amjad**

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the question is incomplete

Thank you Zoha, corrected the typo.

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