A person lends a certain sum of money at 10% per annum simple interest. After 20 years, the total simple interest earned is ₹500 more than the original principal lent. What was the principal amount (in rupees) that was lent?

Introduction:
This question tests forming an equation using simple interest when a relationship between interest and principal is described in words. The key phrase is “interest is ₹500 more than the principal,” which means SI = P + 500. Under simple interest, SI depends linearly on P, r, and t, so we can compute SI in terms of P and equate it to P + 500 to find the principal directly.

Given Data / Assumptions:

• Rate r = 10% per annum
• Time t = 20 years
• Simple interest SI is ₹500 more than principal P
• Formula: SI = (P * r * t) / 100

Concept / Approach:
Compute SI using the formula in terms of P. Then use the word condition SI = P + 500 and solve for P. Because r and t are fixed, SI becomes a constant multiple of P, making the algebra simple.

Step-by-Step Solution:
SI = (P * 10 * 20) / 100 SI = (200P) / 100 = 2P Given SI = P + 500 So 2P = P + 500 P = 500

Verification / Alternative check:
If P = 500, then SI at 10% for 20 years is (500*10*20)/100 = 1000. Interest (1000) is indeed 500 more than principal (500), satisfying the condition exactly.

Why Other Options Are Wrong:
₹250 would give SI=₹500, which is not ₹500 more than ₹250. ₹1,000 would give SI=₹2,000, which is ₹1,000 more than principal, not ₹500. The other values similarly fail the equation 2P = P + 500.

Common Pitfalls:
Misreading “₹500 more than principal” as “₹500 in total,” or accidentally using amount instead of interest in the word condition.

Final Answer:
The principal lent was ₹500.