Practice Questions
Concept Explanation
Depreciation reduces the value of an asset each year at a fixed rate. It follows the compound interest formula with a decrease.
Key Formula
Value after T years = P(1 − R/100)^T
Example
A machine worth Rs. 50,000 depreciates at 10% p.a. After 2 years: 50000 × 0.9^2 = Rs. 40,500.
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Q1 EasyA machine costing Rs. 50,000 depreciates at 10% per annum. Its value after 2 years is:ExplanationFormula: Value after T years = P(1 − R/100)^T. Value = 50000 × (0.9)^2 = 50000 × 0.81 = Rs. 40,500. Hence the answer is Rs. 40,500.
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Q2 EasyThe value of a car is Rs. 1,60,000. It depreciates at 10% per annum. Find its value after 2 years.ExplanationFormula: Value = P(1 − R/100)^T. Value = 160000 × (0.9)^2 = 160000 × 0.81 = Rs. 1,29,600. Hence the answer is Rs. 1,29,600.
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Q3 EasyA machine worth Rs. 1,00,000 depreciates at 10% per annum. Its value after 1 year is:ExplanationFormula: Value = P(1 − R/100). Value = 100000 × 0.9 = Rs. 90,000. Hence the answer is Rs. 90,000.
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Q4 MediumThe value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was:ExplanationFormula: Present value = Purchase price × (1 − R/100)^T. So 8748 = P × (0.9)^3 = P × 0.729 ⇒ P = 8748 / 0.729 = Rs. 12,000. Check: 12000 → 10800 → 9720 → 8748. Hence the purchase price was Rs. 12,000.
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Q5 MediumA machine is purchased for Rs. 80,000. It depreciates at 20% per annum. Its value after 2 years is:ExplanationFormula: Value = P(1 − R/100)^T. Value = 80000 × (0.8)^2 = 80000 × 0.64 = Rs. 51,200. Hence the answer is Rs. 51,200.
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Q6 MediumThe present value of a machine is Rs. 7,290. It depreciates at 10% per annum. Its value 2 years ago was:ExplanationFormula: Past value = Present / (1 − R/100)^T. Past value = 7290 / (0.9)^2 = 7290 / 0.81 = Rs. 9,000. Check: 9000 × 0.81 = 7290. Hence the answer is Rs. 9,000.
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Q7 MediumA scooter costs Rs. 40,000 and depreciates at 5% per annum. Its value after 2 years is:ExplanationFormula: Value = P(1 − R/100)^T. Value = 40000 × (0.95)^2 = 40000 × 0.9025 = Rs. 36,100. Hence the answer is Rs. 36,100.
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Q8 MediumAn equipment bought for Rs. 64,000 depreciates at 25% per annum. Value after 2 years is:ExplanationFormula: Value = P(1 − R/100)^T. Value = 64000 × (0.75)^2 = 64000 × 0.5625 = Rs. 36,000. Hence the answer is Rs. 36,000.
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Q9 MediumA machine depreciates by 10% annually. If its value after 2 years is Rs. 81,000, the original cost was:ExplanationFormula: Original = Present / (1 − R/100)^T. Original = 81000 / (0.9)^2 = 81000 / 0.81 = Rs. 1,00,000. Hence the original cost was Rs. 1,00,000.
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Q10 HardAn asset worth Rs. 27,000 depreciates at 10% every year. Its value after 3 years will be:ExplanationFormula: Value = P(1 − R/100)^T. Value = 27000 × (0.9)^3 = 27000 × 0.729 = Rs. 19,683. Hence the answer is Rs. 19,683.
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Q11 HardA laptop bought for Rs. 60,000 depreciates at 20% in the first year and 10% in the second year. Its value after 2 years is:ExplanationSuccessive depreciation: Value = 60000 × (1 − 20/100) × (1 − 10/100) = 60000 × 0.8 × 0.9 = Rs. 43,200. Hence the answer is Rs. 43,200.
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Q12 HardThe value of a machine decreases by 20% every year. If its present value is Rs. 51,200, its value 2 years ago was:ExplanationFormula: Past value = Present / (1 − R/100)^T. Past value = 51200 / (0.8)^2 = 51200 / 0.64 = Rs. 80,000. Hence the answer is Rs. 80,000.
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Q13 HardRs. 2,00,000 depreciates at 10% per annum for 3 years. The scrap value is:ExplanationFormula: Value = P(1 − R/100)^T. Value = 200000 × (0.9)^3 = 200000 × 0.729 = Rs. 1,45,800. Hence the answer is Rs. 1,45,800.
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Q14 HardA car worth Rs. 5,00,000 depreciates at 15% per annum. Its value after 2 years is:ExplanationFormula: Value = P(1 − R/100)^T. Value = 500000 × (0.85)^2 = 500000 × 0.7225 = Rs. 3,61,250. Hence the answer is Rs. 3,61,250.
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DS1 Easy
What is the machine's value after 2 years?
Statement IThe machine costs Rs. 50,000 and depreciates at 10% per annum for 2 years.
Statement IIThe depreciation rate is 10% per annum.
ExplanationFormula: Value = P(1 − R/100)^T. Statement I alone: Value = 50000 × (0.9)^2 = Rs. 40,500. Statement II alone is incomplete. Statement I alone is sufficient. Answer: A. -
DS2 Medium
A company screening question asks for the value after depreciation. What is the value after 2 years?
Statement IThe initial value of the asset is Rs. 80,000.
Statement IIThe asset depreciates at 20% per annum for 2 years.
ExplanationNeed initial value, rate and time. Statement I alone lacks rate/time. Statement II alone lacks initial value. Together: Value = 80000 × (0.8)^2 = Rs. 51,200. Both are needed. Answer: C.
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DS3 Medium
Is the depreciated value after 2 years less than Rs. 50,000?
Statement IAn asset of Rs. 60,000 depreciates at 20% per annum for 2 years.
Statement IIThe depreciation rate is 20% per annum.
ExplanationStatement I alone: Value = 60000 × (0.8)^2 = Rs. 38,400, which is less than Rs. 50,000, so Yes. Statement II alone cannot decide. Statement I alone is sufficient. Answer: A. -
DS4 Hard
An HR quiz asks for the purchase price of a machine. What was the purchase price?
Statement IPresent value after 3 years of 10% annual depreciation is Rs. 8,748.
Statement IIThe machine depreciates at 10% every year for 3 years.
ExplanationFormula: Purchase = Present / (1 − R/100)^T. Statement I alone already includes present value, rate and time → Purchase = 8748 / 0.729 = Rs. 12,000. Statement II alone lacks present value. Statement I alone is sufficient. Answer: A.