A. B and C together start a business. B invests of 1/6 of the total capital while investments of A and C are equal. If the annual profit on this investment is ? 33600, find the difference between the profits of B and C.

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 rents to be paid by P, Q and R Ratio of monthly equivalent
= (10 x 20) : (30 x 8) : (16 x 9)
= 200 : 240 : 144 = 25 : 30 : 18

Hence R's share
= [18/(25 + 30 + 18)] x 2920
= (18/73) x 2920
= 18 x 40
= ? 720

Let investment of P = ? K
Then, investment of N of = ? (K + 5000)
and investment of M = (K + 5000) + 4000 = ? (K + 9000)

According to the question.
K + (K + 5000) + (K + 9000) = 50000
? 3K + 14000 = 50000
? 3K = 50000 - 14000 = 36000
? K = 36000/3 = 12000

Clearly, investment of P = ? 12000
Investment of N = (K + 5000) = 12000 + 5000 = ? 17000
Investment of M = (K + 9000) = 12000 + 9000 = ? 21000
M's share : N's share : P's share = 21000 : 17000 : 12000
= 21 : 17 : 12

Hence, M's share = [21/(21 + 17 + 12 )] x 70000
= (21/50) x 70000 = ? 29400

Let R's capital = 1
Then, Q's capital = 4
2 (P's capital) = 3 (Q's capital) = 3 x 4 = 12
? P's capital = 12/2 = 6
? P's share : Q's share : R's share = 6 : 4 : 1
Thus, Q's share profit = { 4/(6 + 4 + 1)} x 148500
= (4/11) x 148500
= 4 x 13500
= ? 54000

A's share : B's share : C's share
= Ratio of product of investment and time period of investment
= 4000 x 12 : 8000 x (12 - 3) : 20000 x 2
= 4 x 12 : 8 x 9 : 20 x 2
= 6 : 9 : 5

Let,
A's share = 6N
B's share = 9N
C's share = 5N

According to the question,
6N + 9N + 5N = 16800
? 20N = 16800
? N = 16800/20 = 840

? A's share = 6N = 6 x 840 = ? 5040
B's share = 9N = 9 x 840 = ? 7560
C's share = 5N = 5 x 840 = ? 4200

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

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 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

A's share : B's share : C's share
= (20000 x 12) : (25000 x 4) : (15000 x 8)
= 240000 : 100000 : 120000
= 24 : 10 : 12 = 12 : 5 : 6
Let A's share = 12N
B's share = 5N
C's share = 6N

According to the question.
12N + 5N + 6N = 23000
? 23N = 23000
? N = 23000/23 = 1000
? C's share = 6N = 6 x 1000 = ? 6000

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