Aayush and Babloo are partners in a business. Aayush contributes 1/4 of the capital for 15 months and Babloo received 2/3 of the profit. How long Babloo's money was used?

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

Let B remained in the business for N months. Then,
A : B = (2250 x 12) : (2700 x N)
? 2 : 1 = (27000 : 2700N) = (10 : N)
? 10/N = 2/1 [ ? Ratio of profit is 2 : 1]
? 2N = 10
? N = 10/2 = 5
Clearly, B joined after (12 - 5) = 7 months.

Let the total profit be ? N,
Then, A's share in profit = ? 3N/5
Remaining profit = N - 3N/5 = (5N - 3N) / 5 = 2N/5
? B's share in profit = ? N/5
C's share in profit = ? N/5

According to the question,
(3N/5 - N/5) = 400
2N/5 = 400; N = (400 x 5)/2 = ? 1000

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.

P's share : Q's share = Ratio of their investments
= 13000 : 25000 = 13 : 25

Now, let P's share = 13N
Q's share = 25N

According to the question,
13N + 25N = 76000
? N = 76000/38 = 2000
? Q's share = 25N = 25 x 2000 = ? 50000

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