A starts a business with Rs. 5000 and B joins the business 5 months later with an investment of Rs. 6000. After a year they earn a profit of Rs. 34000, find the shares of A and B in the profit amount depending on their individual investment.

Correct Option: Rs. 20000, Rs. 14000

To find the shares of A and B in the total profit, we need to calculate the ratio of their effective investments over the total period of 1 year (12 months).

Step 1: Calculate the effective investment of A and B

A started the business with Rs. 5000 and stayed for the entire year (12 months).

$\text{Investment of A for 12 months}=5000\times 12=\text{Rs.}60000$

B joined 5 months later with Rs. 6000, which means B's money was invested for (12 - 5) = 7 months.

$\text{Investment of B for 7 months}=6000\times 7=\text{Rs.}42000$

Step 2: Find the ratio of their profits

The profit is divided in the ratio of their effective investments:

$\text{Ratio of profit (A : B)}=60000:42000$

Dividing both terms by 6000, we get:

$\text{Ratio (A : B)}=10:7$

Step 3: Calculate the individual shares from the total profit

Total ratio parts = 10 + 7 = 17 parts.

Total profit = Rs. 34000.

$\text{Share of A}=\frac{10}{17}\times 34000=10\times 2000=\text{Rs.}20000$

$\text{Share of B}=\frac{7}{17}\times 34000=7\times 2000=\text{Rs.}14000$

Therefore, the shares of A and B in the profit amount are Rs. 20000, Rs. 14000.