If the arithmetic mean of 10, 20, 30, 40, 50, …, 180, 190 and 200 is 105, then the arithmeticmean of 20, 40, 60, 80, 100 …, 360, 380 and 400A. is 105B. is 115C. is 210D. cannot be determined
Question
If the arithmetic mean of 10, 20, 30, 40, 50, …, 180, 190 and 200 is 105, then the arithmeticmean of 20, 40, 60, 80, 100 …, 360, 380 and 400A. is 105B. is 115C. is 210D. cannot be determined
Solution
The arithmetic mean, or average, is calculated by adding all the numbers in a set and then dividing by the count of numbers in that set.
In the first series, the numbers are increasing by 10 each time, starting from 10 and ending at 200. The arithmetic mean is given as 105.
In the second series, the numbers are also increasing each time, but by 20, starting from 20 and ending at 400. This is essentially the first series multiplied by 2.
Since multiplication is a linear operation, the mean of the second series will also be the mean of the first series multiplied by 2.
So, the arithmetic mean of the second series is 105 * 2 = 210.
Therefore, the answer is C. is 210.
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