A man lends a sum of money at a simple interest rate of 4% per annum. The total interest earned in 8 years is Rs 340 less than the original principal amount that he lent. Using the simple interest relation and the given difference between principal and interest, find the value of the principal he lent.

Introduction / Context:
This question explores how to connect the simple interest earned over a period of time with the principal when a relationship between the two is given. Instead of providing the interest directly, the problem states that the total interest earned over 8 years is Rs 340 less than the principal. The student must translate this verbal condition into an algebraic equation involving the simple interest formula. Such problems strengthen the ability to interpret words into equations, a key skill in quantitative aptitude.

Given Data / Assumptions:

• Rate of simple interest, R = 4% per annum.
• Time period, T = 8 years.
• Principal lent, P rupees (unknown).
• Total simple interest earned over 8 years is Rs 340 less than the original principal.
• Interest is calculated using simple interest.

Concept / Approach:
The simple interest formula is:
SI = (P * R * T) / 100 The problem states that the simple interest is less than the principal by Rs 340. That means:
P − SI = 340 or equivalently:
SI = P − 340 By substituting SI from the simple interest formula into this relationship, we get an equation with one unknown P. Solving this linear equation yields the required principal.

Step-by-Step Solution:
Let the principal be P rupees. Rate R = 4% per annum, time T = 8 years. Simple interest SI = (P * 4 * 8) / 100 = (32P) / 100 = 0.32P. Given that the interest is Rs 340 less than the principal, so SI = P − 340. Therefore, 0.32P = P − 340. Bring terms together: P − 0.32P = 340. 0.68P = 340. P = 340 / 0.68. P = 500. Hence, the principal lent by the man is Rs 500.

Verification / Alternative check:
For P = Rs 500, simple interest for 8 years at 4% per annum is SI = (500 * 4 * 8) / 100 = 160. Now compare principal and interest: P − SI = 500 − 160 = 340, which matches the condition given in the question. Therefore, the value P = Rs 500 satisfies both the simple interest formula and the relationship between principal and interest.

Why Other Options Are Wrong:
If P = Rs 520, then SI = (520 * 4 * 8) / 100 = 166.4, and P − SI = 353.6, not 340.
If P = Rs 540, then SI = 172.8, and P − SI = 367.2, which does not match 340.
If P = Rs 560, then SI = 179.2, so P − SI = 380.8, again not equal to 340.
If P = Rs 600, then SI = 192, and P − SI = 408, which is different from 340. Thus those options do not satisfy the given condition.

Common Pitfalls:
Learners sometimes misunderstand the phrase “interest is Rs 340 less than the principal” and mistakenly set SI = 340 instead of P − 340. Another frequent error is to compute the amount instead of comparing principal and interest. Algebraic mistakes in combining terms, such as miscomputing 1 − 0.32, can also lead to wrong answers. Writing the relationship clearly before substituting into the simple interest formula helps to avoid confusion.

Final Answer:
The value of the original principal that the man lent is Rs 500.