Q.A, B and C invest $40000$ rupees, $50000$ rupees and $60000$ rupees respectively in a business for one year. The annual profit is $30000$ rupees. Find the share of each partner.

All three capitals are invested for the same year, so the profit is split in the ratio of the capitals.

One part is worth $30000/15 = 2000$ rupees, and each partner takes their number of parts.

This is a simple partnership (equal time for all three partners), so profit is divided in the ratio of the capitals.

Step 1 — form the capital ratio. $40000 : 50000 : 60000 = 4 : 5 : 6 \quad (\text{dividing each by } 10000).$

Step 2 — value of one part. The ratio has $4 + 5 + 6 = 15$ parts, so $\text{one part} = \frac{30000}{15} = 2000 \text{ rupees}.$

Step 3 — each share. $A = 4 \times 2000 = 8000, \quad B = 5 \times 2000 = 10000, \quad C = 6 \times 2000 = 12000 \text{ rupees}.$

Verification. The shares add to $8000 + 10000 + 12000 = 30000$ rupees (the full profit), and their ratio $8000 : 10000 : 12000 = 4 : 5 : 6$ matches the capital ratio — both confirm the answer.

Equivalently, each partner's fraction of the profit is their ratio term over $15$: $A = \frac{4}{15}\times 30000 = 8000$, $B = \frac{5}{15}\times 30000 = 10000$, $C = \frac{6}{15}\times 30000 = 12000$ rupees.

When three or more capitals are given, students sometimes simplify only two of the three numbers before forming the ratio — every term must be divided by the same common factor, so all three capitals here are divided by $10000$ to get $4:5:6$.