Q.C and D are partners with capitals of $40000$ rupees and $60000$ rupees. Interest on capital is allowed at $5\%$ per annum, and D, the working partner, is entitled to a salary of $800$ rupees per month. The remaining profit is shared in the ratio of the capitals. If the annual profit is $19000$ rupees, find the total amount received by each partner.

Interest on capital and D's salary are set aside first; the residual profit is then shared in the capital ratio.

Salary and interest on capital are appropriated before the balance is shared in the capital ratio.

Step 1 — interest on capital (simple interest for one year, so $T = 1$): $C: \frac{40000 \times 5 \times 1}{100} = 2000 \text{ rupees}, \qquad D: \frac{60000 \times 5 \times 1}{100} = 3000 \text{ rupees}.$

Step 2 — D's salary ($800$ rupees per month for $12$ months): $800 \times 12 = 9600 \text{ rupees}.$

Step 3 — total appropriations and residual profit. $\text{Appropriations} = 2000 + 3000 + 9600 = 14600 \text{ rupees},$ $\text{Residual profit} = 19000 - 14600 = 4400 \text{ rupees}.$

Step 4 — share the residual in the capital ratio. The capital ratio is $40000 : 60000 = 2 : 3$ (total $5$ parts), so one part $= \frac{4400}{5} = 880$ rupees, giving $C: 2 \times 880 = 1760, \qquad D: 3 \times 880 = 2640 \text{ rupees}.$ …

Two errors are common: sharing the whole profit of $19000$ in the capital ratio without first deducting the salary and interest, and forgetting to multiply D's monthly salary by $12$ (using $800$ rupees instead of $9600$). Always appropri …