The average of n numbers is 42. If 75% of the numbers are increased by 4 each and the remaining numbers are decreased by 8 each, then what is the average of the numbers, so obtained?

43

Sum of all n numbers = 42n

Change in sum due to increase in 75 % numbers by 4 = 0.75n X 4 = 3n

Change in sum due to decrease in 25 % numbers by 8 = 0.25n X 8 = 2n

New sum of numbers = 42n + 3n - 2n = 43n

So new avg. = \(\frac{43n}{n}\) = 43