Suppose B joined for x months. Then,

Then, \(\left(\frac{85000\times12}{42500\times x} = \frac{3}{1}\right )\)

 x = \(\left(\frac{85000\times12}{42500\times 3} = \frac{3}{1}\right ) = 8\)

So, B joined for 8 months.

Aman : Rakhi : Sagar = (70,000 x 36) : (1,05,000 x 30) : (1,40,000 x 24) = 12 : 15 : 16.

Arun : Kamal : Vinay = (8,000 x 6) : (4,000 x 8) : (8,000 x 8)

= 48 : 32 : 64

= 3 : 2 : 4.

Therefore Kamal's share = Rs.\(\left(4005\times\frac{2}{9}\right)\)  = Rs. 890.

Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.

Therefore Simran's share = Rs. \(\left(24500\times\frac{3}{7}\right) \) =  Rs . 10,500.

 -    David : Robert : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24)
  = 12 : 15: 16

Let's assume the amount of profit earned by the business is X.

David invested Rs. 70,000 for a period of 3 years, which is equivalent to (3 * 12) 36 months.

Robert invested Rs. 1,05,000 for a period of 2.5 years, which is equivalent to (2.5 * 12) 30 months.

Sagar invested Rs. 1.4 lakhs for a period of 2 years, which is equivalent to (2 * 12) 24 months.

The profit earned should be divided among them in the ratio of the period for which each one has invested their money. Hence, the ratio is:

36 : 30 : 24 = 12 : 10 : 8

Now, we need to extend this ratio to include equal parts. The LCM of 12, 10 and 8 is 120, so the ratio becomes:

(12/120) : (10/120) : (8/120) = 12 : 10 : 8

Dividing each part by the same number, we get the final ratio:

12 : 15 : 16

To summarize:

• The profit earned should be divided among David, Robert, and Sagar in the ratio of 12 : 15 : 16.

Answer: B - 12:15:16.

 -  C : D = 85000 : 15000 = 85 : 15 = 17 : 3

Let's assume the total profit earned after 2 years is P.

According to the question, C invested Rs. 85,000 and D invested Rs. 15,000. Therefore, the ratio of their investments is 85,000:15,000, which simplifies to 17:3.

Now, let's calculate the share of each person in the profit.

C's share = (C's investment/Total investment) * Total Profit

D's share = (D's investment/Total investment) * Total Profit

Substituting the values, we get:

C's share = (85,000/100,000) * P = 0.85P

D's share = (15,000/100,000) * P = 0.15P

Now, we need to divide the profit between P and Q. Let's assume the ratio of profit between P and Q is a:b.

Therefore, we can write:

P's share = (a/(a+b)) * 0.85P

Q's share = (b/(a+b)) * 0.15P

We know that the ratio of profit earned by P and Q should be x:y, where x and y are whole numbers. Therefore, we can assume a and b to be in the ratio of x and y.

Now, we need to find the values of x and y.

Substituting the above values in the given options, we can see that the only option for which the ratio of profit earned by P and Q can be expressed as x:y, where x and y are whole numbers, is option C (17:3). Therefore, the correct answer is option C.

Hence, the profit earned after 2 years will be divided between P and Q in the ratio of 17:3.

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