Simple interest on a sum for 6 months at 5% per annum is ₹65.50. What is the principal sum (in rupees)?

Introduction:This question tests calculating principal from simple interest when time is given in months but the rate is per annum. The main skill is converting 6 months into years (0.5 years) so the annual rate can be used correctly in SI = (P * r * t) / 100. Once time is converted, the principal is found by rearranging the formula to P = (SI * 100) / (r * t).

Given Data / Assumptions:

• Simple interest SI = ₹65.50
• Annual rate r = 5% per annum
• Time = 6 months = 6/12 years = 0.5 years
• Principal P = ?
• Formula: SI = (P * r * t) / 100

Concept / Approach:Convert time into years because r is per annum. Substitute SI, r, and t into the formula and solve for P. Carefully handle decimals: 65.50 is a rupee amount, and r is in percent, so keep r as 5 and use division by 100 exactly once.

Step-by-Step Solution: t = 6/12 = 0.5 years SI = (P * r * t) / 100 65.50 = (P * 5 * 0.5) / 100 65.50 = (P * 2.5) / 100 P = 65.50 * 100 / 2.5 P = 6550 / 2.5 = 2620

Verification / Alternative check:If P = 2620, SI for 0.5 years at 5% is (2620*5*0.5)/100 = (2620*2.5)/100 = 65.50, matching exactly.

Why Other Options Are Wrong:₹2600 gives SI = 65.00, slightly short. ₹2880 gives SI = 72.00, too high. ₹1320 is far too low. Only ₹2620 produces SI = ₹65.50 under the given conditions.

Common Pitfalls:Using t = 6 instead of 0.5, treating 5% as 0.05 while still dividing by 100, or rounding 65.50 to 65 and losing accuracy.

Final Answer:The principal sum is ₹2,620.