Multiple choice

Find the correct relationship between the given quantities: Quantity I: The difference between the rate of CI and rate of depreciation if a person Aakash has a sum of INR 2500 which after 3 years at compound interest @20% p.a. becomes a certain amount that is equal to the amount that is the result of 3-year compounded depreciation from INR 8437.5. Quantity II: 5%.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For compound interest at 20% for 3 years on Rs. 2500: Amount = 2500(1.2)³ = 2500(1.728) = Rs. 4320. For depreciation, let the rate be r%. Then 8437.5(1-r/100)³ = 4320. Solving: (1-r/100)³ = 4320/8437.5 = 0.512. Taking cube root: 1-r/100 = 0.8, so r = 20%. Therefore, the depreciation rate is also 20%. The difference between CI rate (20%) and depreciation rate (20%) is 0%. Since 0% < 5%, Quantity II > Quantity I.