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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.