A, B and C start a business each investing ₹20000.After 5 months A withdrew ₹5000, B withdrew ₹4000 and C invests ₹6000 more. At the end of year, a total profit of ₹69900 was recorded. Find the share of each?

Question

Answer

Given Information:

A, B and C invested ₹20000 each in a business.

After 5 months, A withdrew ₹5000, B withdrew ₹4000 and C invested ₹6000 more.

Total profit at the end of the year was ₹69900.

Calculating the profits:

Let the profits of A, B and C be x, y and z respectively.

As A, B and C invested equal amounts, their profit sharing ratio is 1:1:1.

Let the total profit till the time of withdrawals be P.

Then, P = 5/12(x + y + z) * 3 + 7/12(x + y + z) * 12 = (17/12)(x + y + z)

After the withdrawals and additional investment, A, B and C's profits become:

A's profit = (x * 7/12) + [(x - 5000) * 5/12] = 7x/12 - 5x/12 + 5000/12 = x/6 + 416.67

B's profit = (y * 7/12) + [(y - 4000) * 5/12] = 7y/12 - 5y/12 + 2000/12 = y/6 + 166.67

C's profit = (z * 7/12) + [(z + 6000) * 5/12] = 7z/12 + 5z/12 + 5000/12 = z/2 + 416.67

Adding A, B and C's profits, we get:

x/6 + 416.67 + y/6 + 166.67 + z/2 + 416.67 = 69900

x/6 + y/6 + z/2 = 69000

Solving the equations:

From the above equation, we get:

x + y + 3z = 414000

x + y + z = 414000/4 = 103500

Substituting z = (103500 - x - y)/3 in the equation x/6 + y/6 + z/2 = 69000, we get:

x + y = 138000

Using the above two equations, we get:

x = 42000

y = 42000

z = 19500

Final Answer:

A's share = x/4 = ₹10500

B's share = y/4 = ₹10500

C's share = z/4 = ₹4875

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