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Choose the correct option from the followingQuantity I: What is the compound interest available on principal amount of Rs 20,000 at the rate of 12.5% per annum for two years?Quantity II: If an amount of Rs 18,000 is divided in ratio of 5 : 4 wherein larger part is kept at simple interest of 20% for 3 years and smaller part at compound interest of 10% for two years. What is the interest earned by the person at the end of two years?1. Quantity I ≥ Quantity II2. Quantity I ≤ Quantity II3. Quantity I < Quantity II4. Quantity I = Quantity II5. Quantity I > Quantity II |
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Answer» Correct Answer - Option 3 : Quantity I < Quantity II Given: Quantity I : P = Rs 20,000 R = 12.5% (1/8) T = 2 years Quantity II : P = 18,000 Ratio = 5 : 4 Larger part at R = 20% for 3 years S.I. Smaller part at R = 10% for two years C.I. Formula used: Simple interest : (P × R × T)/100 Compound interest : Amount = P (1 + (R/100))n Where, n = Number of years, P = Principal Amount, R = Rate of Interest, A = Amount Calculation: Quantity I : A = 15,000 × (1 + (1/8)) 2 ⇒ A = 15,000 × (9/8) × (9/8) ⇒ A = 25312.5 ⇒ I = 25312.5 – 20000 ⇒ I = 5312.5 Quantity II : P for S.I. = 5 × 18000/9 ⇒ P for S.I. = 10000 ⇒ S.I. = 10000 × 20 × 2/100 (∵ even though this sum is kept for three years question is asked for 2 years) ⇒ S.I. = 4000 P for C.I. = 8,000 ⇒ A = 8000 × (1.10)2 ⇒ A = 9680 ⇒ I = 9680 – 8000 ⇒ I = 1680 ⇒ after two years person will earn interest of Rs 5680 (∵ 4000 + 1680 = 5680) ∴ Quantity I < Quantity II |
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