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The value of a machine depreciates at the rate of 10% per annum. If its present value is ₹1,62,000, then what was the value of the machine 2 years ago?
₹2,00,000
₹2,04,000
₹1,90,000
₹1,86,000
₹2,00,000
Use the ratio method: 10% depreciation means a factor of 0.9. To find the value 2 years ago, divide the present value by (0.9)2, which is 1,62,000/0.81=2,00,000.
Present value of the machine = ₹1,62,000, Rate of depreciation (r) = 10% per annum, Time period (n) = 2 years.
Vp=Va(1−100r)n
Use the ratio method: 10% depreciation means a factor of 0.9. To find the value 2 years ago, divide the present value by (0.9)2, which is 1,62,000/0.81=2,00,000.
Students often apply the depreciation formula forward (multiplying by 0.9) instead of reversing it (dividing by 0.9), leading to a smaller value instead of the larger original value.
Define the relationship
The present value (Vp) is related to the value 2 years ago (Va) by the depreciation formula where n=2 and r=10.
Vp=Va×(1−10010)2
Substitute the values
Plug in the present value 1,62,000 and solve for Va.
1,62,000=Va×(0.9)2
Calculate the initial value
Simplify the equation: 1,62,000=Va×0.81, therefore Va=0.811,62,000.
Va=811,62,000×100=2,00,000
A is correct because the calculated initial value of the machine two years ago is ₹2,00,000.
This concept of 'reverse percentage' is also critical in population growth problems and compound interest calculations where the initial principal is unknown.
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