The average of  n numbers is 45. If 80% of the numbers are increased by 5 each and the remaining numbers are decreased by 10 each, then what is the average of the numbers, so obtained?

47

80% = \(\frac{4}{5}\), Let n = 5, 80% of 5 = 4

Increased by 5 each = 5 × 4 = 20

Remaining 1 is decreased by 10 = 1 × -10 = -10 

Total variation = 20 -10 = 10

This 10 is equally distributed in 5 = \(\frac{10}{5}\) = 2 Average = 45 + 2 = 47