If the compound interest on a certain sum for 2 years is Rs. 308 and the…
2025
If the compound interest on a certain sum for 2 years is Rs. 308 and the simple interest at same rate of interest and for same time is Rs. 280. Find the sum ?
- A.
Rs. 700
- B.
Rs. 1200
- C.
Rs. 1100
- D.
Rs. 500
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Correct Option
Option A: Rs. 700
Step-by-Step Solution
Calculate Annual Simple Interest (SI):
Total Simple Interest for 2 years = Rs. 280.
Annual SI = 280 / 2 = Rs. 140.
Calculate the Difference between Compound Interest (CI) and SI:
CI for 2 years = Rs. 308.
Difference = CI - SI = 308 - 280 = Rs. 28.
Note: This difference represents the interest earned on the first year's interest.
Find the Rate of Interest (R):
The difference (Rs. 28) is the interest earned on the first year's SI (Rs. 140).
Rate (R) = (Difference / Annual SI) * 100 = (28 / 140) * 100 = 20%.
Calculate the Principal (Sum):
Using the SI formula: SI = (Principal * Rate * Time) / 100.
140 = (Principal * 20 * 1) / 100.
140 = Principal * 0.2.
Principal = 140 / 0.2 = Rs. 700.