Two persons K and L enter into a business by investing their capitals in the ratio 7 : 9. L leaves the business after 7 months, and at the end of 11 months the total profit is Rs. 2460. What is L's share of the profit in rupees?

Introduction / Context:
This is a standard partnership question in which two partners invest in a certain ratio, but one partner withdraws earlier than the other. The profits are therefore not shared in simple proportion to the capitals but in proportion to capital multiplied by time. The task is to compute the share of L given the total profit and the time for which each partner remains in the business.

Given Data / Assumptions:

• Capital ratio of K to L is 7 : 9.
• Total duration of the business is 11 months.
• K stays invested for the full 11 months.
• L leaves the business after 7 months.
• Total profit at the end of 11 months is Rs. 2460.
• Profits are shared in proportion to capital multiplied by time.

Concept / Approach:
In partnership problems where partners are active for different durations, we use the concept of capital time units. Each partner's effective contribution is capital amount multiplied by the number of months he or she stays in the business. The ratio of these products directly determines the ratio of profits. Once we form this ratio, we can calculate each partner's share from the known total profit. This eliminates the need to know the exact actual amount of capital and works entirely with proportional values.

Step-by-Step Solution:
Step 1: Let the common capital factor be k. Then K invests 7k and L invests 9k. Step 2: K remains in the business for 11 months, so K's capital time units are 7k * 11 = 77k. Step 3: L remains in the business for 7 months, so L's capital time units are 9k * 7 = 63k. Step 4: The ratio of profit shares is therefore 77k : 63k, which simplifies to 77 : 63. Step 5: Divide both terms by 7 to obtain 11 : 9 as the final ratio. Step 6: Total profit is Rs. 2460, which is divided in the ratio 11 : 9, that is 20 equal parts. Step 7: Value of one part is 2460 / 20 = Rs. 123. Step 8: L's share corresponds to 9 parts, so L's profit is 9 * 123 = Rs. 1107.

Verification / Alternative check:
We can verify by checking K's share too. K obtains 11 parts, so his profit is 11 * 123 = Rs. 1353. Adding both shares, 1353 + 1107 = Rs. 2460, which matches the given total profit. This confirms that the ratio and the value of one part were computed correctly, and that L's share of Rs. 1107 is accurate.

Why Other Options Are Wrong:
The amounts Rs. 1109, Rs. 1111, Rs. 1113 and Rs. 1095 do not maintain the correct ratio of 11 : 9 when paired with the remaining profit for K. For example, if L received Rs. 1113, then K would receive 2460 minus 1113, that is Rs. 1347, and the ratio 1347 : 1113 would not simplify to 11 : 9. Only Rs. 1107 gives a complementary amount of Rs. 1353 for K, which fits exactly the correct profit sharing ratio.

Common Pitfalls:
A frequent mistake is to ignore the fact that L leaves early and to divide the profit according to the simple capital ratio 7 : 9, which would be incorrect. Another pitfall is miscalculating the number of months or mixing up 7 months and 11 months. Some learners also attempt to work with actual capital amounts without realising that a simpler proportional approach using a variable factor k is enough. Always remember that partnership profit problems depend on both capital and time together.

Final Answer:
L's share in the profit at the end of 11 months is Rs. 1107, which corresponds to option B.