Three friends A, C and D entered into a partnership. A invested 1.5 times more than that of D and C invested 20% of the amount invested by A. If the overall profit at the end of the year is Rs. 2400, then find the profit share of D (in Rs.).

To find the profit share of D, we first need to determine the ratio of the investments of the three partners, A, C, and D, since the profit share is directly proportional to the investment when the time period is the same for all partners.

Let the amount invested by D be $x$.
According to the problem, A invested 1.5 times more than D. This means A's investment is D's investment plus 1.5 times D's investment:
Investment of A = $x+1.5x=2.5x$

C invested 20% of the amount invested by A:
Investment of C = $20\%\text{of}2.5x=0.20\times 2.5x=0.5x$

Now, let's write down the ratio of their investments (A : C : D):
$\text{A : C : D}=2.5x:0.5x:x$
Dividing by $x$, we get:
$\text{A : C : D}=2.5:0.5:1$
Multiplying all terms by 2 to convert decimals into whole numbers, we get:
$\text{A : C : D}=5:1:2$

The total ratio parts are:
$5+1+2=8$

Given that the overall profit at the end of the year is Rs. 2400, the profit share of D is calculated as:
$\text{Profit share of D}=\frac{2}{8}\times 2400$
Simplifying the expression:
$\text{Profit share of D}=\frac{1}{4}\times 2400=600$

Thus, the profit share of D is Rs. 600.