Aman invested ₹(P + 3000) for 3 years at 8% simple interest. Anuj invested an amount of ₹P for 2 years at 12% compound interest and received the same amount of interest as Aman received. Find the amount that is invested by Anuj.
Answer & explanation
Correct answer: option 2
As per the Question,
Simple interest for Aman = Compound interest for Anuj
(P+3000)×8×3/100 = [P(1 + 12/100)^2] - P
(P+3000)×8×3/100 = [P(112/100)^2] - P
(P+3000)×8×3/100 = P/10000[(112)^2 - (100^2)]
(P+3000)×8×3×100 = P[(112)^2 - (100^2)]
(P+3000)×2400 = P[(112+100) (112-100)]
(P+3000)×2400 = P[(212×12)]
(P+3000)×2400 = P[2544]
2544P - 2400P =3000×2400
144P = 3000×2400
P = 50000
The correct answer is Option (2) → ₹50,000