Question

An assertion reason type questions consists of two statements; an assertion (statement of fact) and a reason (explanation for the given assertion). First you have to determine whether each statement is correct or not. If both the statements are correct, then you have to determine whether the reason support the assertion.

In assertion reason Questions, four options are given as follows:

(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
(B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
(C) Assertion is correct but Reason is incorrect
(D) Assertion is incorrect but Reason is correct OR Assertion and Reason both incorrect.

Assertion : If the mean of five observations x , x + 2 , x + 4, x + 6, x + 8 is 11, then mean of last three observations is 8. Reason : Mean of n observations = Sum of observations / Number of observations

(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
(B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
(C) Assertion is correct but Reason is incorrect
(D) Assertion is incorrect but Reason is correct .​

Answer 1

Answer:

mean

sum off all points / number of all points

→ x + x + 2 + x + 4 + x + 6 + x + 8/5 = 11

→ 5x + 20 /5 = 11

→ 5x + 20 = 11×5 = 55

→ 5x = 55 - 20 = 35

→ x = 35/5 = 7

→ x = 7

therefore, numbers are

x = 7

x + 2 = 9

x + 4 = 11

x + 6 = 13

x + 8 = 15

so mean of last three observation

→ 11 + 13 + 15 /3

→ 39/3 = 13

mean is 13 not 8.

therefore, option D is correct

assertion is incorrect but reason is correct

hope this answer helps you dear!

Answer 2

Given Question

In assertion reason Questions, four options are given as follows:

(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

(B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

(C) Assertion is correct but Reason is incorrect.

(D) Assertion is incorrect but Reason is correct OR Assertion and Reason both incorrect.

Assertion : If the mean of five observations x , x + 2 , x + 4, x + 6, x + 8 is 11, then mean of last three observations is 8.

Reason : Mean of n observations = Sum of observations / Number of observations

(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

(B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

(C) Assertion is correct but Reason is incorrect.

(D) Assertion is incorrect but Reason is correct .

$\large\underline{\sf{Solution-}}$

Given set of observations are

$\rm :\longmapsto\:x , \: x + 2 , \: x + 4, \: x + 6, \: x + 8$

and

$\rm :\longmapsto\:Mean = 11$

We know that

$\\ \rm :\longmapsto\:\boxed{\tt{ Mean = \dfrac{Sum \: of \: obervation}{Number \: of \: observations}}}$

So, on substituting the values, we get

$\rm :\longmapsto\:11 = \dfrac{x + x + 2 + x + 4 + x + 6 + x + 8}{5}$

$\rm :\longmapsto\:11 = \dfrac{5x + 20}{5}$

$\rm :\longmapsto\:5x + 20 = 55$

$\rm :\longmapsto\:5x = 55 - 20$

$\rm :\longmapsto\:5x = 35$

$\rm :\longmapsto\:x = 7$

So, observations are

$\rm :\longmapsto\:7,9,11,13,15$

So, Mean of last three observations 11, 13, 15 is

$\rm :\longmapsto\:Mean = \dfrac{11 + 13 + 15}{3}$

$\rm :\longmapsto\:Mean = \dfrac{39}{3}$

$\bf\implies \:Mean = 13$

$\bf\implies \:Assertion \: is \: not \: correct \: but \: reason \: is \: correct$

$\bf\implies \:Option \: (d) \: correct$