The arithmetic mean of three numbers is 6, if the first number is 2.5 times more, and the second is 1.5 times more than the third.

Let’s denote the first number as x, the second as y, and the third as c, respectively. Then, from the problem statement, we know that the arithmetic mean of these three numbers is 6. That is, we get an expression of the following form:

(x + y + c) / 3 = 6;
x + y + c = 18

It is also known that the first number is 2.5 times larger than the second:

x = 2.5y

And the second is 1.5 times more than the third:

y = 1.5s;
c = y / (1.5)

Let’s plug everything into the first equation:

2.5y + y + y / 1.5 = 18;
3.5y + y / 1.5 = 18;
y (3.5 + 0.7) = 18;
y = 4.32

Then:

x = 2.5y = 2.5 * 4.32 = 10.8;

c = y / (1.5) = 4.32 / 1.5 = 2.88