A and B started a business jointly. A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received ₹ 4000 as profit, then their total profit is:

### Concept & Formula The profit share is directly proportional to the product of capital invested and time period of investment. $$Ratio of Profit = (Capital_A \times Time_A) : (Capital_B \times Time_B)$$ ### Step-by-Step Solution 1. Let B's investment be $x$ and the period of B's investment be $y$. 2. Then, A's investment is $3x$ and the period of A's investment is $2y$. 3. Find the ratio of their profits: A : B = $(3x \times 2y) : (x \times y) = 6xy : xy = 6 : 1$. 4. This means out of every 7 parts of profit, A gets 6 parts and B gets 1 part. 5. We are given that B's profit share (1 part) is ₹ 4000. 6. The total profit consists of 7 parts (6 parts for A + 1 part for B). 7. Total profit = $7 \times 4000 = 28000$. ### Exam Strategy & Shortcut Multiply the ratios directly: Investment ratio is 3:1. Time ratio is 2:1. Profit ratio = $3 \times 2 : 1 \times 1 = 6:1$. Total profit is $6+1=7$ times B's profit. $7 \times 4000 = 28000$. ### Common Pitfall Finding A's profit (24000) and incorrectly choosing that as the final answer instead of summing A and B for the *total* profit. ### Final Answer Therefore, the correct answer is **₹ 28000**.