Q.A invests $8000$ rupees in a business. After $6$ months he withdraws $2000$ rupees. B invests $6000$ rupees for the whole year. If the annual profit is $2600$ rupees, find each partner's share.

A's capital changes partway through the year, so his contribution is computed stretch by stretch before the ratio is formed.

A's capital does not stay fixed for the year — it is $8000$ rupees for the first $6$ months and then $8000 - 2000 = 6000$ rupees for the last $6$ months — so his contribution must be found stretch by stretch.

Step 1 — A's total capital-months. $A = (8000 \times 6) + (6000 \times 6) = 48000 + 36000 = 84000.$

Step 2 — B's total capital-months. B keeps $6000$ rupees for all $12$ months: $B = 6000 \times 12 = 72000.$

Step 3 — form and reduce the ratio. $84000 : 72000 = 7 : 6 \quad (\text{dividing both by } 12000).$

Step 4 — value of one part. Total parts $= 7 + 6 = 13$, so $\text{one part} = \frac{2600}{13} = 200 \text{ rupees}.$ …

A frequent mistake is to use A's final capital of $6000$ rupees for the whole year, or his initial $8000$ rupees for the whole year — neither is correct. The withdrawal spl …