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.).

The correct answer is 600.

Let the amount invested by D be Rs. $x$.

According to the question, A invested 1.5 times more than that of D. This means the investment of A is:

$\mathrm{Investment\; of\; A}=x+1.5x=2.5x$

C invested 20% of the amount invested by A. Thus, the investment of C is:

$\mathrm{Investment\; of\; C}=20\%of2.5x=0.2\times 2.5x=0.5x$

Since the investment duration for all three partners is the same, the ratio of their profit shares will be equal to the ratio of their investments:

$\mathrm{Ratio}(A:C:D)=2.5x:0.5x:x$

To simplify the ratio into integers, we can divide each term by $x$ and then multiply by 2:

$A:C:D=5:1:2$

The sum of the ratio parts is:

$5+1+2=8$

The total overall profit at the end of the year is Rs. 2400. Therefore, the profit share of D is:

$\mathrm{Profit\; share\; of\; D}=\left(\frac{2}{8}\right)\times 2400$

$\mathrm{Profit\; share\; of\; D}=\frac{1}{4}\times 2400=600$

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