A man lends a sum of money at a simple interest rate of 4% per annum. If the total interest earned in 8 years is Rs. 340 less than the original principal amount, find the value of the principal he lent.

Introduction / Context:
This problem focuses on relating simple interest and principal when there is a given difference between them. Instead of directly providing the value of interest, the question states that the interest for a certain period is 340 rupees less than the principal. The learner must use the simple interest formula to connect principal, rate, time, and interest, then incorporate the given relationship between interest and principal. This style of question appears often in bank exams and general aptitude tests.

Given Data / Assumptions:
Rate of simple interest r is 4 percent per annum.
Time period t is 8 years.
Simple interest for 8 years is 340 rupees less than the principal P.
Interest is computed using simple interest, not compound interest.
All values are in rupees and the rate is per annum.

Concept / Approach:
The formula for simple interest is I = P * r * t / 100. Here, I is not given directly but related to P through I = P - 340, since interest is 340 rupees less than principal. By substituting the expression for I from the simple interest formula and equating it with P - 340, we obtain a linear equation in P. Solving this equation yields the principal. This is a standard algebraic manipulation of the simple interest formula.

Step-by-Step Solution:
Let the principal amount be P rupees.Simple interest for 8 years at 4 percent per annum is I = P * 4 * 8 / 100.Simplify to get I = P * 32 / 100 = 0.32P.According to the question, this interest is 340 rupees less than the principal, so I = P - 340.Set the two expressions for I equal: 0.32P = P - 340.Rearrange to get P - 0.32P = 340, so 0.68P = 340.Solve for P by dividing both sides by 0.68: P = 340 / 0.68 = 500.Thus, the principal lent by the man is Rs. 500.

Verification / Alternative check:
With P = 500 rupees, compute interest using the simple interest formula. Interest I equals 500 * 4 * 8 / 100 = 500 * 32 / 100 = 160 rupees. The principal minus interest is 500 - 160 = 340 rupees. This matches the condition that interest is 340 rupees less than the principal, confirming that P = 500 is consistent with the data. Therefore the solution is correct.

Why Other Options Are Wrong:
If P were 520 rupees, interest at 4 percent for 8 years would be 520 * 32 / 100 = 166.4 rupees, and the difference between principal and interest would not be exactly 340 rupees.
For P = 540 rupees or P = 560 rupees, performing similar calculations yields differences that are not equal to 340 rupees.
P = 600 rupees gives interest 192 rupees and a difference of only 408 rupees, again not matching the condition of 340 rupees.

Common Pitfalls:
Some learners mistakenly set interest equal to 340 rather than principal minus 340. Others confuse this relationship and write I = 340 - P, which is incorrect. It is also easy to make arithmetic errors while simplifying the decimal coefficient 0.32 or while isolating P. Working carefully step by step and checking the equation with the final value of P helps avoid mistakes.

Final Answer:
The principal amount lent by the man is Rs. 500.