Q.A invests $12000$ rupees for $8$ months and B invests $16000$ rupees for $9$ months in a business. The profit at the end is $20000$ rupees. Find each partner's share.

The two capitals are invested for different times, so profit is shared in the ratio of capital x time (capital-months).

The times differ ($8$ months for A, $9$ months for B), so this is a compound partnership and profit is shared in the ratio of capital × time.

Step 1 — capital-months for each partner. $A: 12000 \times 8 = 96000, \qquad B: 16000 \times 9 = 144000.$

Step 2 — form and reduce the ratio. $96000 : 144000 = 2 : 3 \quad (\text{dividing both by } 48000).$

Step 3 — value of one part. Total parts $= 2 + 3 = 5$, so $\text{one part} = \frac{20000}{5} = 4000 \text{ rupees}.$ …

Directly as fractions: $A = \frac{96000}{240000}\times 20000 = 8000$ and $B = \frac{144000}{240000}\times 20000 = 12000$ rupees, where …

Students sometimes share the profit in the ratio of the capitals alone ($12000:16000 = 3:4$) and ignore the different times — whenever the periods of investment differ, it …