If at same rate of interest, in 2 years, the simple interest is ₹56 and compound interest
is ₹72, then what is the principal (in ₹)?
Correct Answer:
C. 49
Explanation:
The correct answer is Option C: 49.
To find the principal, we first determine the difference between the compound interest (CI) and simple interest (SI) for the 2-year period. The difference is ₹72 - ₹56 = ₹16. In simple interest, the interest earned each year is equal, so the interest for the first year is ₹56 / 2 = ₹28. The difference of ₹16 between CI and SI in the second year represents the interest earned on the first year's interest. Therefore, the interest rate (R) is (16 / 28) * 100, which simplifies to 400/7%.
Finally, using the simple interest formula SI = (P * R * T) / 100, we substitute the known values: 56 = (P * (400/7) * 2) / 100. Solving for P, we get 56 = (P * 800) / 700, which simplifies to 56 = 8P / 7. Multiplying both sides by 7 gives 392 = 8P, and dividing by 8 results in a principal (P) of ₹49.
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