The average of n number is 45. If 60% of the number are increased by 5 each and the remaining numbers are decreased by 10 each, then what is the average of the number so obtained?

Solution (By Examveda Team)

$$\eqalign{ & {\text{Average of }}n{\text{ numbers}} = 45 \cr & {\text{Let, }}n = 100 \cr & {\text{New average}} \cr & = \frac{{100 \times 45 + 60 \times 5 - 40 \times 10}}{{100}} \cr & = \frac{{100 \times 45}}{{100}} + \frac{{300 - 400}}{{100}} \cr & = 45 - 1 \cr & = 44 \cr} $$