The arithmetic mean (i. e., average) of a set of 7 numbers is 20. the mean of a second set of 13 numbers is 40. what is the mean of all 20 numbers?

The mean of the first set of 7 numbers is 20.
Therefore the sum of the 7 numbers is
S₁ = 7*20 = 140

The mean of the second set of 13 numbers is 40.
Therefore the sum of the 13 numbers is
S₂ = 13*40 = 520

The sum of the two sets of numbers is
S = S₁ + S₂ = 140 + 520 = 660

Altogether, there are 7+13 = 20 numbers.
The overall mean of the 20 numbers is
660/20 = 33

The mean of all 20 numbers is 33.