A is a working and B is a sleeping partner in a business. A puts in Rs. 12,000 and B Rs. 20,000. A receives 10% of the profit for managing, the rest being divided in proportion to their capitals. Out of a total profit of Rs. 9600 the money received by A is?

Sanjay's investment for 1 months = 15000 x 12 = Rs. 180000
Komal's investment for 1 months = 15000 x 8 + (15000 - 10000) x 4
= 120000 + 20000
= Rs. 140000

? Ratio between the investment of Sanjay and Komal
= 180000 : 140000 = 9 : 7
? Sanjay's profit = [9/(9 + 7)] x 32000 = Rs. 18000

Let the total profit be Rs. 100
After paying to Charity,
A's share = Rs. 95 x (3/5) = Rs. 57
If A's share is Rs. 57, then total profit = Rs. 100
If A's share is Rs. 855, then total profit = Rs. 855 x (100/51) = Rs. 1500

? Ratio of shares = (9000 x 12) : (8000 x 7) = 108 : 56 = 27 : 14
? Sudhakar's share = Rs. 6970 x (14/41) = Rs. 2380

A : B : C = Rs. (16000 x 3 + 11000 x 9) : (12000 x 3 + 17000 x 9) : (21000 x 6)
= 147 : 189 : 126
= 7 : 9 : 6
? (B's share) - (C's share) = Rs. [ 26400 x (9/22) - 26400 x (6/22)]
= Rs. (10800 - 7200) = Rs. 3600

Ratio of profits of A and B = 5/7 : 2/7 = 5 : 2
? (16000 x 8)/(N x 4) = 5/2
? 20N = 256000
? N = 128000
So, B contributed Rs. 12800.

Ratio of rent = 6 : 10 : 12 = 3 : 5 : 6
? Pandeyji has to pay = Rs. 350 x (6/14) = Rs. 150

Total profit - Remuneration = Balance profit This balance profit is divided in proportion to their investment
? (Balance Profit of A) / (Balance Profit of B) = (Investment of A) / (investment of B)
? (390 - 10 x 12) / balance of Profit of B = 3000/4000 = 3/4
(Since remuneration of A is Rs. 10 per month)
? Balance profit of B = (4 x 270)/3 = Rs. 360
Since B does not get any remuneration, hence B receives Rs. 360 at the end of the year.

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 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

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