A and B started a business by investing ? 20000 and ? 25000, respectively. After 4 months B left and C joined by investing ? 15000. At the end of the year, there was a profit of ? 23000 What is C's share?

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
? 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
? 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
? 12N = 33600
? N = 33600/12 = 2800
? Difference in the profits of B and C
= 5N - 2N = 3N = 3 x 2800 = ? 8400

Let investment of A = N,
Investment of B = 2N,
Investment of C = 3N,

? A's share : B's share : C's share
= (N x 12) : (2N x 6) : (3N x 4)
= 12N : 12N : 12N
= 1 : 1 : 1

? C's share = [1/(1 + 1 + 1)] x 54000
= (1/3) x 54000 = ? 18000

Ratio of equivalent capitals of A, B and C = (35000 x 12) : (20000 x 5) : (15000 x 7)
= 35 x 12 : 20 x 5 : 15 x 7
= 84 : 20 : 21
Let A's share = 84N
B's share = 20N
C's share = 21N
According to the question,
84N + 20N + 21N = 84125
? 125N = 84125
? N = 84125/125 = 673
? B's share = 20N = (20 x 673) = ? 13460

Q gets 2/7 of the profit.
? P gets(1 - 2/7) = 5/7 of the profit
? P : Q = 5/7 : 2/7 = 5 : 2
Let the contribution of Q be a.
Then, 8000 x 8 : a x 4 = 5 : 2
? 64000/4a = 5/2
? 20a = 128000
? a = 128000/20 = ? 6400

Let the annual profit be ? N Then, ? (N - 120) will be distributed between A and B as their shares of profit.
Ratio of profits = Ratio of investments So, A : B = 3000 : 4000 = 3 : 4
? A's share = 120 + (N - 120) x 3/7
? 120 + (N - 120) x 3/7 = 390
? (N - 120) x 3/7 = 390 - 120 = 270
? N - 120 = (270 x 7)/3 = 630
? B's share = 4/7 x (N - 120)
= (4/7) x 630 = ? 360

Let investment of Amit = 12k
and investment of Brijesh = 11k
Let Brijesh invested the money for N months.

Then,
Amit's investment : Brijesh's investment
= (12k x 11) : (11k x N) = 132k : 11kN = 12 : N
? 12/N = 4/1 [ ? ratio of profit is 4 : 1]
? 4N = 12
? N = 12/4 = 3 months
Clearly, Brijesh invested money for 3 months.

Given. ratio = 7/2 : 4/3 : 6/5
= (7/2) x 30 : (4/3) x 30 : (6/5) x 30
= 105 : 40 : 36

Let investment of Amitabh = 105k
Investment of Kamlesh = 36k

Ratio of their investments
= [105k x 4 + 150% x8 of 105k] : (40k x 12) : (36k x 12)
= (420k + (150/100) x 105k x 8) : (480k) : (432k)
= (1680k) : (480k) : (432k)
= 35 : 10 : 9

? Brijesh's share
= (21600 x 10) / (35 + 10 + 9)
= (21600 x 10) / 54
= ? 4000