A and B entered into a partnership investing ₹ 16000 and ₹ 12000 respectively. After 3 months, A withdrew ₹ 5000 while B invested ₹ 5000 more. After 3 more months, C joins the business with a capital of ₹ 21000. The share of B exceeds that of C, out of a total profit of ₹ 26,400 after one year by

### Concept & Profit Distribution In a partnership, if investments are made for different time periods, the profit is distributed in the ratio of the product of capital and time for each partner. $$ \text{Profit Ratio} = (C_1 \times T_1) : (C_2 \times T_2) : (C_3 \times T_3) $$ ### Step-by-Step Solution * **A's Investment:** Invests ₹ 16000 for 3 months. Then withdraws ₹ 5000, leaving ₹ 11000 for the remaining 9 months. * A's equivalent capital = $(16000 \times 3) + (11000 \times 9) = 48000 + 99000 = 147000$ * **B's Investment:** Invests ₹ 12000 for 3 months. Then invests ₹ 5000 more, making it ₹ 17000 for the remaining 9 months. * B's equivalent capital = $(12000 \times 3) + (17000 \times 9) = 36000 + 153000 = 189000$ * **C's Investment:** Joins after 6 months (3 months + 3 more months) with ₹ 21000. So, C's money is invested for $12 - 6 = 6$ months. * C's equivalent capital = $21000 \times 6 = 126000$ * **Profit Ratio:** * $A : B : C = 147000 : 189000 : 126000$ * Dividing by 1000: $147 : 189 : 126$ * Dividing by 21: $7 : 9 : 6$ * **Total Profit:** ₹ 26400 * Total ratio parts = $7 + 9 + 6 = 22$ parts * Difference between B's and C's shares is $(9 - 6) = 3$ parts. * Difference = $\frac{3}{22} \times 26400 = 3 \times 1200 = 3600$ ### Exam Strategy & Shortcut Instead of calculating B's and C's shares individually and then subtracting, directly calculate the difference in their ratio parts (9 - 6 = 3 parts) and find the value of those 3 parts relative to the total profit. ### Common Pitfall Miscalculating the number of months each partner's money is invested. Carefully read phrases like "After 3 more months" to determine the total elapsed time before a new event occurs. ### Final Answer Therefore, the correct answer is **₹ 3600**.