Question

the average of 15 numbers is 7. angelo is adding these numbers and mistakenly reads 6 of the numbers as 9 instead of seven, what average will he get?

Answer 1

if the average of 15 numbers is 7, the sum should be $15*7=105$
if for 6 of the numbers, he sees 9 instead of 7, he is counting 2 additional units per number, so his sum will be greater by $2*6=12$, therefore the sum he gets is $105+12=117$ 
from that, the average he calculates is $\frac{117}{15} = 7.8$