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**Hint:**The profits are shared in the ratio of one’s investment. The investment made by the individuals are calculated and based on that ratio of their investment are calculated. The profit is shared as per the ratio of their investment.

**Complete step-by-step answer:**

Investment made by A for 1 year, ${I_A} = 2000$

Investment made by B for 2 year,

\[

{I_B} = 2 \times 3000 \\

{I_B} = 6000 \\

\]

Investment made by C for 2 year,

$

{I_C} = 2 \times 4000 \\

{I_C} = 8000 \\

$

The ratio of their investment is given by

${I_A}:{I_B}:{I_C} = 2000:6000:8000$

To simplify the ratio divide it by 1000,

${I_A}:{I_B}:{I_C} = 2:6:8$

Now again to simplify divide the ratio by 2,

${I_A}:{I_B}:{I_C} = 1:3:4$

The total parts of this investment $ = 1 + 3 + 4 = 8$

A’s share in the investment is 1 out of the 8 parts; B’s share is 3 out of 8 while C’s share is 4.

Therefore, the profit share of A’s investment of Rs. 2000$ = \dfrac{1}{8} \times 3200 = 400$.

**Hence, the correct option is (D).**

**Note:**It is important to note that profits are shared in the ratio of the investment. If the share is less then the profit will be less and vice versa.

For instance if the ratio of the investment is $1:2:3$ and the net profit is 3000 Rs. then

A’s share $ = \dfrac{1}{6} \times 3000 = 500$

B’s share $ = \dfrac{2}{6} \times 3000 = 1000$

C’s share $ = \dfrac{3}{6} \times 3000 = 1500$

The ratio of the profit shared between A, B and C is given by,

\[

{P_A}:{P_B}:{P_C} = 500:1000:1500 \\

{P_A}:{P_B}:{P_C} = 1:2:3 \\

\]

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