The simple interest on a certain principal amount for 4 years at 10% per annum…
2023
The simple interest on a certain principal amount for 4 years at 10% per annum is half of the compound interest on ₹ 1000 for 2 years at 20% per annum. Find the principal amount
Answer: D. ₹550 — ConceptSimple interest is calculated only on the original principal: SI = Prt/100, where P is principal, r is the annual rate, and t is time in years.…
- A.
₹500
- B.
₹450
- C.
₹650
- D.
₹550
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Correct answer: D
Concept
Simple interest is calculated only on the original principal: SI = Prt/100, where P is principal, r is the annual rate, and t is time in years.
Compound interest uses the amount formula A = P(1 + r/100)n and CI = A − P. When one interest is a stated fraction of another, first compute the known interest and then form the equation.
Application
For ₹1000 at 20% per annum for 2 years, the compound amount is A = 1000(1 + 20/100)2 = 1000 × 1.44 = ₹1440.
Therefore, the compound interest is ₹1440 − ₹1000 = ₹440, so half of it is ₹220.
Let the required principal be P. Its simple interest for 4 years at 10% per annum is SI = P × 10 × 4/100 = 0.4P.
Equating the two interest values gives 0.4P = 220, hence P = 220/0.4 = ₹550.
Cross-check
For ₹550, simple interest at 10% per annum for 4 years is ₹550 × 10 × 4/100 = ₹220.
This equals half of ₹440, confirming that the required principal is ₹550.