P and Q entered a partnership for 3 yr. At the start of the business, they invested ? 13000 and ? 25000, respectively. At the end of 3 yr their total profit was ? 76000. What will be share of Q out of this profit?

Ratio of total capital of A and B = 20000 x 12 : 35000 x 12
= 240000 : 420000

Now, C gives ? 220000 to both to make the capital equal.
? A's capital : B's capital = 240000 + 200000 : 420000 + 200000
= 440000 : 440000

If A takes ? 200000 and B takes ? 20000 from C, then both have the equal capital
? Required ratio of divided amount
= 200000 : 20000
= 20 : 2 = 10 : 1

Hence. A and B should divide the amount in the ratio of 10 : 1.

Let the total capital be ? R and Babloo's money is used for N months.
Capital of Aayush = R/4
? Capital of Babloo = (R - R/4) = 3R/4

Ratio of investments of Aayush and Babloo
= (R/4) x 15 : (3R/4 x b) = 15/4 : 3N/4 = 5 : N

Ratio of profits of Aayush and Babloo = (1/3) : (2/3) = 1 : 2
? 5/N = 1/2
? N = 10 months

Hence, Babloo's money was used for 10 months.

For management, money received by Anil = 10% of 9000 = ? 900
Balance = ? (9000 - 900) = ? 8100
Now, ratio of investments =12000 : 20000 = 3 : 5

? Anil's share = ? 8100 x 3/(3 + 5)
= ? 8100 x 3/8 = ? 3037.50

? Amount received by Anil = ? 900 + 3037.50
= ? 3937.50

Let investment of Aarti during first year = 5a
Investment of Vinita during first year = 7a
Investment of kamla during first year = 6a

Then, their investments during second year are
? (126/100) x 5a : (120/100) x 7a : (115/100) x 6a
= 630 : 840 : 690 = 21 : 28 : 23

Here, P₁ : P₂ : P₃ = 2 : 3 : 5 [profit's ratio]
and x₁ : x₂ : x₃ = 4 : 6 : 9 [investment's ratio]

According to the rule,
Required ratio = P₁/x₁ : P₂/x₂ : P₃/x₃
= 2/4 : 3/6 : 5/9
= 1/2 : 1/2 : 5/9 = 9 : 9 : 10

Ratio of profits of Rajan and Sajan = Ratio of their investments
=14200 : 15600 = 142 : 156 = 71 : 78

? Rajan's share = [71/(71 + 78)] x 74500
= (71/149) x 74500
= ? 35500

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

Let initial investment be 3k, 5k and 7k rupees.
? (3k - 45600) : 5k : (7k + 337600) = 24 : 59 : 167
? (3k - 45600)/5k = 24/59
? k = 47200
? Initial investment of A = Rs. (47200 x 3) = Rs. 141600

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.

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