The average of 18 numbers is 37.5. If six numbers of average X are added to them, then the average of all the numbers increases by one, The value of x is:
Sum of the 18 numbers = 37.5 $$\times 18 = 675
($$\because$$ average = $$\frac{sum of total terms}{number of terms}$$)
Sum of the 6 numbers = 6 $$\times$$ X = 6X
Average of all the numbers = 37.5 + 1 = 38.5
$$\frac{675 + 6X}{24}$$ = 38.5$$
675 + 6X = 24 $$\times$$ 38.5
6X = 924 - 675 = 249
X = 41.5
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