Two persons contribute Rs. 5000 and Rs. 4000 towards partnership. They agree to divide the profit upto the 8% of the total capital equally amongst themselves and further agrees that the excess if…

Solution to the Partnership Profit Division Problem

Step 1: Calculate Total Capital

The total capital invested by the two partners is: $$5000+4000=\text{Rs. }9000$$

Step 2: Determine 8% of Total Capital

The partners agree to divide the profit up to 8% of the total capital equally: $$8\%\text{ of }9000=0.08\times 9000=\text{Rs. }720$$ Since the total profit is Rs. 1800, which is greater than Rs. 720, the first Rs. 720 is divided equally.

Step 3: Divide the First Portion (Rs. 720) Equally

Each partner receives: $$\frac{720}{2}=\text{Rs. }360$$

Step 4: Calculate Remaining Profit

The remaining profit after dividing Rs. 720 is: $$1800-720=\text{Rs. }1080$$

Step 5: Divide the Remaining Profit in the Ratio of Their Capitals

The ratio of their investments is: $$5000:4000=5:4$$ Total parts = $5+4=9$.

Now, divide Rs. 1080 in the ratio 5:4:

• First partner’s share: $$\frac{5}{9}\times 1080=\text{Rs. }600$$
• Second partner’s share: $$\frac{4}{9}\times 1080=\text{Rs. }480$$

Step 6: Total Share of Each Partner

• First partner (Rs. 5000 investor): $$360+600=\text{Rs. }960$$
• Second partner (Rs. 4000 investor): $$360+480=\text{Rs. }840$$

Final Answer

The profit of Rs. 1800 should be divided as follows:

• First partner (Rs. 5000 investor) receives Rs. 960
• Second partner (Rs. 4000 investor) receives Rs. 840