A man borrows some money from a private organisation at 5% simple interest per annum. He lends the same money to another person at 10% compound interest per annum, compounded yearly. After 4 years, he makes a profit of Rs 26,410 from this transaction. How much money did he originally borrow?

Introduction / Context:
This question combines simple interest and compound interest in a single profit scenario. The man acts as an intermediary: he borrows at a lower simple interest rate and lends at a higher compound interest rate. His profit arises from the difference between what he receives and what he must repay after 4 years. This type of problem tests multi concept reasoning and the ability to model a real world financial transaction mathematically.

Given Data / Assumptions:

He borrows principal P from an organisation at 5 percent simple interest per annum
He lends the same principal P to another person at 10 percent compound interest per annum, compounded yearly
Total duration of both borrowing and lending is 4 years
His net profit after 4 years is Rs 26,410
We assume no other fees or charges, only the stated interest flows

Concept / Approach:
First, compute the amount he must repay to the organisation after 4 years under simple interest: amount_out = P + P * 0.05 * 4. Next, compute the amount he receives from the borrower under compound interest for 4 years at 10 percent: amount_in = P * (1.10)^4. The profit is the difference amount_in minus amount_out. Set this equal to 26,410 and solve for P. This results in a linear equation because the compound factor (1.10)^4 is constant.

Step-by-Step Solution:
Step 1: Express the amount he must repay at simple interest. Simple interest rate = 5 percent per annum. Time T = 4 years. Simple interest on borrowing = P * 0.05 * 4 = 0.20 * P. Amount he repays to organisation = P + 0.20 * P = 1.20 * P. Step 2: Express the amount he receives under compound interest. Compound interest rate = 10 percent per annum. Compounding yearly for 4 years gives factor (1.10)^4. So amount received from borrower = P * (1.10)^4. Step 3: Compute (1.10)^4. (1.10)^2 = 1.21 and (1.10)^4 = (1.21)^2 = 1.4641. Thus amount_in = P * 1.4641. Step 4: Express profit as difference between amounts. Profit = amount_in - amount_out = P * 1.4641 - P * 1.20. Profit = P * (1.4641 - 1.20) = P * 0.2641. Step 5: Set profit equal to 26,410 and solve for P. 0.2641 * P = 26,410. P = 26,410 / 0.2641 = 100,000 rupees.

Verification / Alternative check:
To verify, assume P = Rs 1,00,000. Simple interest over 4 years at 5 percent is 1,00,000 * 0.05 * 4 = 20,000 rupees, so he must repay 1,20,000 rupees. Under 10 percent compound interest for 4 years, the amount received is 1,00,000 * 1.4641 = 1,46,410 rupees. The profit is 1,46,410 - 1,20,000 = 26,410 rupees, exactly as stated. This confirms that the original borrowed amount is indeed Rs 1,00,000.

Why Other Options Are Wrong:
If P were Rs 1,50,000 or Rs 2,00,000, the profit would scale proportionally and be significantly greater than 26,410 rupees. If P were Rs 1,32,050, the profit would be 0.2641 * 1,32,050, which does not equal 26,410. Only P = 1,00,000 rupees produces the exact profit of 26,410 under the given simple and compound interest conditions.

Common Pitfalls:
Some candidates mistakenly apply simple interest to both sides of the transaction or compound interest to both sides, losing the key asymmetry that generates profit. Others subtract the rates directly without accounting for the different interest calculation methods. A further error is miscomputing the compound factor (1.10)^4. It is important to compute the two amounts separately using the correct formulas and then subtract them to obtain the profit.

Final Answer:
The man originally borrows Rs 1,00,000 from the private organisation.