ganga and atri start an enterprise by investing rs 24000 and rs 36000 respectively. their agreement is to share half of the total profit equally and then share the remaining half in the ratio of their capitals. if they share the entire profit in the ratio of their capitals atri would have got rs 2500 more than what she would have got otherwise. what is the total profit?
Let's break down the information given step-by-step to solve the problem:
Step 1: Given information
Ganga invests Rs 24,000 and atri invests Rs 36,000.
They agree to share half of the total profit equally and then share the remaining half in the ratio of their capitals.
Step 2: Calculate the profit sharing ratio
Since they agree to share the remaining half of the profit in the ratio of their capitals, we need to calculate their ratio.
The ratio of Ganga's capital to atri's capital is 24000:36000 = 2:3.
Step 3: Calculate the difference in profit sharing
According to the given information, if they share the entire profit in the ratio of their capitals, atri would get Rs 2500 more than what she would have gotten otherwise.
So, the difference in profit sharing is Rs 2500.
Step 4: Calculate the remaining profit after equal sharing
Let's assume the total profit to be x.
Since they agree to share half of the profit equally, the profit to be shared equally is x/2.
Step 5: Calculate the profit to be shared in the ratio
The remaining half of the profit, x/2, will be shared in the ratio of their capitals, which is 2:3.
So, Ganga's share will be (2/5)*(x/2) and atri's share will be (3/5)*(x/2).
Step 6: Calculate the difference between their actual and proposed share
According to the given information, atri would get Rs 2500 more if they share the profit in the ratio of their capitals compared to the proposed equal sharing.
So, (3/5)*(x/2) - (1/2)*(x/2) = 2500.
Step 7: Solve the equation
Simplifying the equation from Step 6:
(3/10)*x - (1/4)*x = 2500
(12/40)*x - (10/40)*x = 2500
(2/40)*x = 2500
(1/20)*x = 2500
x = 2500 * 20
x = 50000
Therefore, the total profit is Rs 50,000.
To solve this problem, we need to find the total profit. Let's break down the information given to us:
1. Ganga and atri invested Rs 24,000 and Rs 36,000 respectively.
2. They agree to share half of the total profit equally.
3. They also agree to share the remaining half in the ratio of their capitals.
4. If they share the entire profit in the ratio of their capitals, atri would have received Rs 2,500 more than if they had followed the agreed-upon distribution.
Let's proceed step by step to find the total profit:
Step 1: Calculate the share of each person if they share half of the profit equally.
Since they invest in the ratio of 2:3 (24,000:36,000), the ratio of their shares would be 2:3 as well.
To find their share, we divide half of the total profit in the ratio 2:3:
Ganga's share = (1/2) * Total profit * (2/5)
atri's share = (1/2) * Total profit * (3/5)
Step 2: Calculate the share of each person if they share the remaining half in the ratio of their capitals.
Since we know the share of each person in this case, we can use the given information to calculate their shares.
According to the problem statement, if they share the entire profit based on their investments, atri would receive Rs 2,500 more than she would have otherwise. This implies that her share is Rs 2,500 more than what she would receive under the agreed-upon distribution.
Let's say that atri would receive X under the agreed distribution. Then we can write the following equation:
(X + 2,500) = atri's share if they share the remaining half based on their investments
Step 3: Equate the two equations and solve for X.
By equating the two equations, we can find the value of X, which represents atri's share under the agreed distribution.
(Ganga's share) + (atri's share) = (Ganga's share if they share based on capital) + (atri's share if they share based on capital)
[(1/2) * Total profit * (2/5)] + [(1/2) * Total profit * (3/5)] = (1/2) * Total profit + X
Simplify the equation:
[(2/10) + (3/10)] * Total profit = (1/2) * Total profit + X
Simplifying further:
(5/10) * Total profit = (1/2) * Total profit + X
Multiply both sides by 10 to eliminate the fraction:
5 * Total profit = 5 * (1/2) * Total profit + 10X
5 * Total profit = (5/2) * Total profit + 10X
Multiply through by 2 to eliminate the fraction:
10 * Total profit = 5 * Total profit + 20X
10 * Total profit - 5 * Total profit = 20X
5 * Total profit = 20X
Total profit = 20X / 5
Total profit = 4X
Step 4: Solve for X to find the value of the total profit.
We know that atri would have received X under the agreed-upon distribution. So, the total profit will be four times the value of X.
Looking back at the problem statement, it states that atri would have received Rs 2,500 more if they shared the total profit based on their capital ratio. This implies that X = 2,500.
Therefore, the total profit = 4 * X = 4 * 2,500 = Rs 10,000.
Hence, the total profit is Rs 10,000.
Ganga received $X.
atri received (36,000/24,000) * x = $1.5x.
x + 1.5x = P, X = 0.4P.
x + (1.5x-2500) = 0.5P.
Replace X with 0.4P:
0.4P + 0.6P = 0.5P + 2500, P = $5000. = Total profit.
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