A starts a cement trading business by investing Rs 5 lakhs. After 2 months B joins the business by investing Rs 10 lakhs, and 4 months after B joins, C also joins by investing Rs 20 lakhs. One year after A started the business the total profit is Rs 350000. What is the share of B in the profit in rupees?

Introduction / Context:
This question describes a partnership where partners join at different times with different capitals. The business runs for one year from the time A starts. B and C join later with larger capitals. Profit is to be shared according to capital multiplied by the time for which each capital remained invested. We must calculate B effective contribution in money months and use it to find B share from the total profit of Rs 350000.

Given Data / Assumptions:
A invests Rs 5 lakhs at the start of the business. B joins after 2 months investing Rs 10 lakhs. C joins 4 months after B, which is 6 months after A, investing Rs 20 lakhs. Total time from A start to profit calculation is 12 months. Total profit after 1 year is Rs 350000.

Concept / Approach:
The key idea is money months. We treat capitals in lakhs or rupees consistently over the periods they are invested. A is in the business for the full 12 months, B for 10 months and C for 6 months. We compute capital * time for each partner, which gives the relative weights for sharing the profit. Profit is then divided in the ratio of these money months. Finally, we apply this ratio to the total profit to find B share.

Step-by-Step Solution:
Step 1: Use capitals in lakhs for simplicity. A capital = 5, B capital = 10, C capital = 20. Step 2: Time for A is full year = 12 months. Step 3: Time for B is from month 2 to month 12, that is 10 months. Step 4: Time for C is from month 6 to month 12, that is 6 months. Step 5: Money months for A = 5 * 12 = 60 units. Step 6: Money months for B = 10 * 10 = 100 units. Step 7: Money months for C = 20 * 6 = 120 units. Step 8: Ratio of contributions A : B : C = 60 : 100 : 120. Step 9: Simplify ratio by dividing all terms by 20, giving 3 : 5 : 6. Step 10: Total ratio parts = 3 + 5 + 6 = 14 parts. Step 11: Value of one part of profit = 350000 / 14. Step 12: Compute 350000 / 14 = 25000. Step 13: B share corresponds to 5 parts, so B share = 5 * 25000 = Rs 125000.

Verification / Alternative check:
We can find shares of A and C to confirm correctness. A share = 3 * 25000 = Rs 75000. B share = 5 * 25000 = Rs 125000. C share = 6 * 25000 = Rs 150000. Sum of all shares is 75000 + 125000 + 150000 = 350000, which matches the total profit. The ratio 75000 : 125000 : 150000 simplifies by dividing by 25000 to 3 : 5 : 6, confirming that money month ratio has been applied correctly.

Why Other Options Are Wrong:
If B share were Rs 75000, Rs 100000 or Rs 150000, the corresponding ratio among A, B and C would not match 3 : 5 : 6 given the fixed total profit. For example, Rs 150000 for B would make B equal to or larger than C in a way inconsistent with the capital time contributions. Only Rs 125000 ensures all shares are proportional to 3 : 5 : 6 and sum to Rs 350000.

Common Pitfalls:
Learners may mistakenly use 12 months for all three partners or miscount the months between joining times. Another frequent error is forgetting to simplify the money months correctly before extracting the ratio. Some also misread the phrase 4 months after B joins and assume C joins 4 months from the start. Carefully counting months from A start and forming capital * time products solves such partnership timing questions reliably.

Final Answer:
B share of the profit from the cement trading business is Rs 125000.