Reena and Shaloo are partners in a business. Reena invests Rs. 35,000 for 8 months and Shaloo invests Rs. 42,000 for 10 months. Out of a total profit of Rs. 31,570, what is the share of Reena?

Introduction / Context:
This question is a typical two partner partnership problem with different investment amounts and different investment periods. We must calculate the effective investments for Reena and Shaloo using capital * time, derive the ratio in which they should share the profit and then compute Reena's exact share from the total profit of Rs. 31,570.

Given Data / Assumptions:

• Reena invests Rs. 35,000 for 8 months.
• Shaloo invests Rs. 42,000 for 10 months.
• Total profit at the end of the period is Rs. 31,570.
• Profit is shared in proportion to capital * time.
• The entire period is assumed to be continuous with no mid period withdrawals.

Concept / Approach:
The concept used is effective investment. Because the partners invest for different numbers of months, we cannot simply compare their capitals. Instead we multiply each partner's capital by the number of months it is invested. The profit is then split in the ratio of these effective investments. Finally, we apply this ratio to the known total profit to calculate Reena's share.

Step-by-Step Solution:
Step 1: Compute Reena's effective investment: 35,000 * 8 = 2,80,000 rupee months. Step 2: Compute Shaloo's effective investment: 42,000 * 10 = 4,20,000 rupee months. Step 3: Write the ratio of effective investments: Reena : Shaloo = 2,80,000 : 4,20,000. Step 4: Simplify this ratio by dividing both terms by 1,40,000: 2,80,000 / 1,40,000 = 2, 4,20,000 / 1,40,000 = 3. So the ratio becomes 2 : 3. Step 5: Total ratio parts = 2 + 3 = 5. Step 6: Each part of profit = 31,570 / 5 = 6,314. Step 7: Reena gets 2 parts, so Reena's share = 2 * 6,314 = Rs. 12,628. Step 8: Shaloo's share would be 3 * 6,314 = Rs. 18,942.

Verification / Alternative check:
Verify by adding the two shares: 12,628 + 18,942 = 31,570, which matches the total profit. The ratio of Reena's share to Shaloo's share is 12,628 : 18,942. Dividing both by 6,314 gives 2 : 3, which is exactly the ratio of their effective investments. This confirms that the profit has been correctly divided.

Why Other Options Are Wrong:
Values such as 18,245, 11,235 and 10,253 do not maintain the 2 : 3 ratio when combined with the remaining profit for Shaloo. For example, if Reena received 18,245, the remaining profit for Shaloo would be 13,325 and the ratio would not be 2 : 3. Hence those options do not align with the partnership rule of capital * time proportionality.

Common Pitfalls:
Students sometimes use only the capitals 35,000 and 42,000 and ignore the different durations of 8 and 10 months. Another mistake is to reverse the ratio or miscalculate the simplified form. Always double check by simplifying the ratio carefully and ensuring that the sum of individual shares equals the total profit.

Final Answer:
Reena's share of the profit is Rs. 12,628.