A profit of Rs 103500 has to be divided between three partners A, B and C in the ratio 11 : 7 : 5. How much amount in rupees does B receive?

Introduction / Context:
This question is a direct application of ratio distribution for profits among three partners. The total profit is given along with the ratio of shares. We are asked to find the amount received by one specific partner, B. Such problems build fluency in converting ratio parts into actual monetary values by using simple proportion methods.

Given Data / Assumptions:
Total profit to be divided is Rs 103500. Ratio of profit shares of A, B and C is 11 : 7 : 5. We must find the share of B. All three partners are assumed to be entitled to profit exactly in this ratio with no other adjustments.

Concept / Approach:
The ratio 11 : 7 : 5 represents how the total profit is split among A, B and C. The sum of the ratio parts tells us into how many equal parts the total profit is conceptually divided. Each partner share is then the product of the number of parts associated with that partner and the value of one part. For B we simply take 7 parts out of the total number of parts.

Step-by-Step Solution:
Step 1: Ratio A : B : C is 11 : 7 : 5. Step 2: Sum of ratio parts = 11 + 7 + 5 = 23. Step 3: Value of one part = total profit / total parts = 103500 / 23. Step 4: Compute 103500 / 23 = 4500. Step 5: B share equals 7 parts. Step 6: Share of B = 7 * 4500 = Rs 31500.

Verification / Alternative check:
We can also compute shares of A and C to validate the distribution. Share of A = 11 * 4500 = Rs 49500. Share of C = 5 * 4500 = Rs 22500. The total of all three shares is 49500 + 31500 + 22500 = 103500, which exactly matches the given total profit. Also, the ratio 49500 : 31500 : 22500 simplifies to 11 : 7 : 5 when divided by 4500, confirming that the calculations preserve the intended ratio.

Why Other Options Are Wrong:
Rs 22500 is the share of C, not B, based on 5 parts of the ratio. Rs 49500 is the share of A, corresponding to 11 parts. Rs 50500 does not match any partner share and would make the total exceed the given 103500 or change the ratio. Only Rs 31500 corresponds to 7 parts out of 23 and fits the given ratio and total.

Common Pitfalls:
Learners sometimes forget to sum the ratio correctly or miscalculate the value of one part. Another frequent error is misidentifying which ratio number belongs to which partner. Writing the ratio clearly, labelling each term with A, B and C, and checking that the final shares add up to the total profit helps avoid such mistakes.

Final Answer:
B receives a profit share of Rs 31500.