A and B started a joint business. A's investment was thrice the investment of B and the period of his investment was twice the period of investment of B. If B got ? 6000 as profit, then what will be the 20% of total profit?

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

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.

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

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

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

A's share : B's share : C's share
= [16000 x 3 + (16000 - 5000) x 9] : [12000 x 3 + (12000 + 5000) x 9] : (21000 x 6)
= (16 x 3 + 11 x 9) : (12 x 3 + 17 x 9) : (21 x 6)
= 147 : 189 : 126
= 7 : 9 : 6

Hence, B's share exceeds C's share by = {13200/(7 + 9 + 6)} x (9 - 6)
= (13200 x 3)/22
= ? 1800

The difference counts only due to 40% of the profit which was distributed according to their investments.

Let total profit = R.
40% of R is distributed in the ratio, 125000 : 85000 = 25 : 17

Share of 1st partner = 40% of R x25/(25 + 17)
= 40% of 25R/42 = (40/100) x (25R/42) = 5R/21

Share of 2nd partner
= 40% of 17R/42 = (40/100) x (17R/42) = 17R/105

Now according to the question
5R/21 - 17R/105 = 600
? R(25 - 17)/105 = 600
? R = (600 x 105)/8
= ? 7875

Let us assume the ratio factor is x.
According to question,
Quantity of milk = 4x liters and Quantity of Water = x liters.
According to question,
4x + x = 45
? 5x = 45
? x = 9
Quantity of milk = 4x = 9 x 4 = 36 liters
Quantity of water = x = 9 liters
Let y liters of water be added to make the ratio 3:2
Then,
36/(9 + y) = 3/2
? 72 = 27 + 3y
? y = 15 liters
If you add 15 liters of water, the ratio will become 3:2.

Let us assume the number of boys = B and number of girls = G.
According to question,
B + G = 30
Lets us assume total weight of boys = W1 and total weight of girls = W2
average weight of boys = total weight of boys/number of boys
total weight of boys/number of boys = 20
W1/B = 20
W1 = 20B

average weight of girls = total weight of girls/number of girls
25 = W2/G
W2 = 25G

Data is not sufficient to solve the equation.
since we do not know either the average weight of the whole class or the ratio of no. of boys to girls.

Method 1 to solve the equation.
Let us assume Cost Price (C.P) of 1 liter milk be Y rupees.
According to question,
Selling Price (S.P) of 1 liter of mixture Y rupees. (Selling price should be same as Cost price)
Profit = 50/3 %
Let us assume Cost price of 1 Liter of Mixture of Water and Milk = C
Cost price of 1 Liter of Mixture of Water and Milk = Selling price of Mixture - Profit
C = Y - C x 50/3%
? C = Y - C x 50/3x100
? C = Y - C x 1/3x2
? C = Y - C/6
? Y = C + C/6
? Y = (6C + C)/6
? Y = (6C + C)/6
? Y = 7C/6
? C = 6Y/7
Since in Y rupees we will get 1 liter milk.
Hence in 1 rupees we will get 1/Y liter milk.
Hence in 6Y/7 rupees we will get 1 x 6Y/7 x Y liter milk.
Hence in 6Y/7 rupees we will get 6/7 liter milk.
We need 1 liter mixture of milk and water for sold on the same price, we need to mix the water.
So water quantity in mixture = 1 - 6/7 = 1/7

Ratio of Milk and water in mixture = quantity of Milk in Mixture/quantity of Water in Mixture
Ratio of Milk and water in mixture = 6/7 / 1/7
Ratio of Milk and water in mixture = 6 x 7 / 7
Ratio of Milk and water in mixture = 6 / 1
Ratio of Milk and water in mixture = 6 : 1

Method 2 to solve the question.
Let the original amount of milk be 1 liter and the cost price is 1 rupees per liter.
Cost price of milk = 1 rupees.
Selling price of Mixture = 1 rupees.
When the milk is mix with x liters of water milk remaining is 1- x.
Let us assume the cost price of milk in mixture is Y and given that the Sold Price is 1.
we should use the Profit formula in algebra,
Y + Y x 50/3 % = 1
Y + Y x 50/3 x 100 = 1
Y + Y x /3 x 2 = 1
7Y/6 = 1
Y = 6/7
Y = 6/7 is the cost price of Mixture for 1 liter.
Since water is free so there is not cost of water in mixture. So price of milk is 6/7 rs in mixture.
Since as per question,
In 1 rupees we will get 1 liter of milk.
hence in 6/7 rupees we will get 1 x 6/7 = 6/7 liter of milk.
Now we have to make 1 liter of mixture with water and milk.
quantity of Water + Quantity of Milk = 1 liter
quantity of Water + 6/7 = 1
quantity of Water = 1 - 6/7 = (7 - 6)/7
quantity of Water = 1/7
Ratio of milk and Water = Quantity of Milk / quantity of Water
Ratio of milk and Water = (6/7) / (1/7)
Ratio of milk and Water = (6/7) x (7/1)
Ratio of milk and Water = 6 x 7/ 7 x 1
Ratio of milk and Water = 6 :1