Let required ratio of investments be
I₁ : I₂ : I₃.
Ratio of investments = Ratio of profits
2I₁ : I₂ : 8I₃ = 3 : 4 : 2
Taking first two terms of the ratio
(2I₁) / I₂ = 3/4
⇒ I₁ / I₂ = 3/8 = 6/16
⇒ I₁ : I₂ = 6 : 16
Taking last two terms of the ratio ,
I₂ / (8I₃) = 4/2

Correct Option: A

Let required ratio of investments be
I₁ : I₂ : I₃.
Ratio of investments = Ratio of profits
2I₁ : I₂ : 8I₃ = 3 : 4 : 2
Taking first two terms of the ratio
(2I₁) / I₂ = 3/4
⇒ I₁ / I₂ = 3/8 = 6/16
⇒ I₁ : I₂ = 6 : 16
Taking last two terms of the ratio ,
I₂ / (8I₃) = 4/2
⇒ I₂/I₃ = 16/1
⇒ I₂ : I₃ = 16 : 1
∴ I₁ : I₂ : I₃ = 6 : 16 : 1

Let total profit = N
Paid to charity = 9% of N = 9N/100
∴ Balance profit = N - (9N/100) = 91N/100
∴ A's share = [4/(4 + 3)] x (91N/100) = (4/7) x (91N/100)

According to the question,
(4/7) x (91N/100) = 1196

Correct Option: A

Let total profit = N
Paid to charity = 9% of N = 9N/100
∴ Balance profit = N - (9N/100) = 91N/100
∴ A's share = [4/(4 + 3)] x (91N/100) = (4/7) x (91N/100)

According to the question,
(4/7) x (91N/100) = 1196
∴ N = (1196 x 7 x 100)/(4 x 91) = ₹ 2300
Hence, total profit = ₹ 2300

Let total profit = N
Paid to charity = 5% of N = (5 x N)/100 = N/20
∴ Balance profit = N - N/20 = 19N/20
∴ A's share = (19N/20) x (3/5) = 57N/100

According to the question.
57N/100 = 4275

Correct Option: C

Let total profit = N
Paid to charity = 5% of N = (5 x N)/100 = N/20
∴ Balance profit = N - N/20 = 19N/20
∴ A's share = (19N/20) x (3/5) = 57N/100

According to the question.
57N/100 = 4275
∴ N = (4275 x 100)/57 = 7500
Hence. total profit = ₹ 7500

Given, Investment of B = 1/6 of total capital
∴ Investments of A and C each = 1/2(1 - 1/6) of total capital
= (1/2) x (5/6) of total capital
= (5/12) of total capital

Now. A's share : B's share : C's share = (5/12) : (1/6) : (5/12) = 5 : 2 : 5
Let A's share = 5N
B's share = 2N
C's share = 5N

According to the question.
5N + 2N + 5N = 33600

Correct Option: A

Given, Investment of B = 1/6 of total capital
∴ Investments of A and C each = 1/2(1 - 1/6) of total capital
= (1/2) x (5/6) of total capital
= (5/12) of total capital

Now. A's share : B's share : C's share = (5/12) : (1/6) : (5/12) = 5 : 2 : 5
Let A's share = 5N
B's share = 2N
C's share = 5N

According to the question.
5N + 2N + 5N = 33600
∴ 12N = 33600
∴ N = 33600/12 = 2800
∴ Difference in the profits of B and C
= 5N - 2N = 3N = 3 x 2800 = ∴ 8400

Suppose A invests Rs. N/6 for M/ 6 months. B invests Rs. N/3 for M/3 months and C invests Rs. [N - (N/6 + N/3)]
For M months.
Ratio of their investment = (N/6 x M/6) : (N/3 x M/3) : (N / 2NM)

Correct Option: A

Suppose A invests Rs. N/6 for M/ 6 months. B invests Rs. N/3 for M/3 months and C invests Rs. [N - (N/6 + N/3)]
For M months.
Ratio of their investment = (N/6 x M/6) : (N/3 x M/3) : (N / 2NM)
= 1/36 : 1/9 : 1/2 = 1 : 4 : 18
∴ B's share = Rs. 4600 x (4/23) = Rs. 800