The average of eight numbers is 6. If each number is multiplied by 5, then the average of the new set of numbers is 

30

Let no.s are = a, b, c, d, e, f, g, h

average of numbers = \(\frac{a\;+\;b\;+\;c\;+\;d\;+\;e\;+\;f\;+\;g\;+\;h}{8}\) =6 (given)

Now, if we multiplied the numbers by 5, then new numbers are = 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h

average of new numbers = \(\frac{5a\;+\;5b\;+\;5c\;+\;5d\;+\;5e\;+\;5f\;+\;5g\;+\;5h}{8}\) = \((5\frac{a\;+\;b\;+\;c\;+\;d\;+\;e\;+\;f\;+\;g\;+\;h}{8})\) = 5 × 6 = 30

Hence new average will be = 30

Direct approach : *If we multiply the actual numbers by n, then new average will n times of old average.*

Therefore,

Numbers are multiplied by 5, then new average = 6 × 5 = 30