arun sharma Averages

Question

answer is A please explain

Answer 1

Let us assume the number be 'x'.

Then the average of 5 consecutive numbers which is given as 'n' will be equal to:

n = ((x) + (x+1) +(x+2) + (x+3) + (x+4)) / 5

n = ((5*x) + 10)/5

n = (x+2)  -----> Equation 1

Now, if the next two numbers in the consecutive series are also included, then the new average (let it be 'Avg') will be equal to:

Avg = ((x) + (x+1) +(x+2) + (x+3) + (x+4) + (x+5) + (x+6)) / 7

Avg = ((7*x) + 21)/7

Avg = (x+3)  -----> Equation 2

Then, from Equations 1 & 2:

-> The new average 'Avg' is 1 greater than the old average 'n'. 

i.e., The new Average is increased by 1.

Hence, the answer is (a).

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Answer 2

Or you may take example like take 5 consecutive no .i.e. 1 to 5 .now ((1+2+3+4+5)/5) so avg of this is 3. Now take next avg including next two consecutive no. ((1+2+3+4+5+6+7)/7)=4 . Now we can compare that new avg. is 1 greater than the old avg.