If A and B get profits of Rs. 6000 and Rs. 4000 respectively at the end of…

Concept: In a partnership, if all partners invest for the same length of time, the share of profit each partner receives is proportional to the capital (investment) each has put in — Profit ∝ Investment × Time. When Time is common to every partner, it cancels out of the proportionality, leaving: Profit ratio = Investment ratio.

1. A and B both invested for the same period (till the end of the year), so time is common to both and cancels out of the ratio.

2. A's profit = Rs. 6000 and B's profit = Rs. 4000, so the investment ratio is Investment(A) : Investment(B) = 6000 : 4000.

3. Divide both terms by their HCF, 2000: 6000/2000 : 4000/2000 = 3 : 2.

Cross-check: If the investments were split in 3 parts to 2 parts of a common unit x, A would invest 3x and B would invest 2x; over the same time period their profits would be in the ratio 3x : 2x = 3 : 2, which matches Profit(A) : Profit(B) = 6000 : 4000 = 3 : 2 exactly.

So the ratio of A's and B's investments is 3:2.