Question : Directions: The value of a certain product depreciates at the rate of 20% every year. It was purchased 3 years ago. If its present value is INR 10,000, then what was the approximate purchase price of the product?
Option 1: INR 15,237
Option 2: INR 19,531
Option 3: INR 18,145
Option 4: INR 25,000
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Correct Answer: INR 19,531
Solution :
Given:
Let the purchasing value of the product 3 years ago = P
Depreciation rate = 20% every year
Time = 3 years
Equivalent depreciation rate for 3 years –
Equivalent rate for 2 years = (20 + 20) - {(20 × 20) ÷ 100} = 40 – (400 ÷ 100) = 40 – 4 = 36%
Equivalent rate of 36% and 20% = (36 + 20) – {(36 × 20) ÷ 100} = 56 – (720 ÷ 100) = 56 – 7.2 = 48.8%. Thus, the product value has been depreciated by 48.8% in 3 years
Remaining value = 100 – 48.8 = 51.2%
Present value = Rs. 10,000
51.2% of P = (51.2 ÷ 100) × P
Similarly,
51.2% of 10,000 = 10,000 ÷ 0.512 P
= 19531.25 ~ 19531
Thus, the product's value 3 years ago was Rs. 19531. Hence, the second option is correct.
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