Simple Interest – Infer principal from difference in interest rates: The difference between simple interest at 13% per annum and 12% per annum on the same sum for 1 year is Rs 110. Find the principal.
Aptitude
Simple Interest
Difficulty: Easy
Choose an option
Answer
Correct Answer: Rs 11000
Explanation
Introduction / Context:At simple interest, interest is P * r * t. For the same P and t, the difference between two interest rates over 1 year directly equals P multiplied by the rate gap.
Given Data / Assumptions:
- Rate1 = 13% per annum
- Rate2 = 12% per annum
- Time = 1 year
- Difference in SI = Rs 110
Concept / Approach:Difference = P * (0.13 - 0.12) * 1 = 0.01 * P. Hence P = Difference / 0.01.
Step-by-Step Solution:
0.01 * P = 110P = 110 / 0.01 = Rs 11000Verification / Alternative check:
At 12%: SI = 1320; at 13%: SI = 1430; difference = 110 (consistent)Why Other Options Are Wrong:
- Rs 12000 / Rs 13000 / Rs 16000 / Rs 10000: produce differences other than Rs 110 when multiplied by 1%.
Common Pitfalls:
- Using percentage points incorrectly.
- Confusing difference in rate with ratio of rates.
Final Answer:Rs 11000.