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Explanation
A and B are partners in a business.
A contributes 1/4 of the capital for 15 months.
B received 2/3 of the profit.
Let suppose the total capital is “y” and A & B’s investment in a business should be y/4 and 3y/4 respectively.
- A’s total investment for 15 months = 15y/4
- B’s total investment for z (say) months = 3yz/4
Let suppose the total profit is “p” and A & B’s profit should be p/3 and 2p/3 respectively.
Now we know the formula which would be used to calculate the required duration of B’s investment;
B’s share in profit = (B’s share in capital x total profit)/total ratio
By substituting values of B’s share in profit (2p/3), B’s share in capital (3yz/4), total profit (p) and total ratio [15y/4 + 3yz/4 = (15y + 3yz)/4] we can calculate the value of “z” (the required duration of B’s investment = 10 months).
To Find
Duration of B’s investment = ?
Solution
Let suppose;
Total capital = y
A’s investment (given: 1/4 of the capital) = y/4
B’s investment = y – y/4 = 3y/4
A’s total investment for 15 months = 15y/4
B’s total investment for z (say) months = 3yz/4
Let suppose;
Total profit = p
B’s profit (given: 2/3 of the profit) = 2p/3
A’s profit = p – 2p/3 = p/3
Now according to the formula;
2p/3 = (3yz x p)/4 / (15y + 3yz)/4
2p/3 = (3yz x p) / (15y + 3yz)
2p x (15y + 3yz) = 3 x (3yzp)
30py + 6yzp = 9yzp
30p + 6zp = 9zp
30p = 9zp – 6zp
30p = 3zp
30 = 3z
z = 30/3
z = 10 months answer
Conclusion
A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. B’s money was used for 10 months.
