Mathematics for FinancePYQ Nov. 20Question 1438 of 512
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Present value of a scooter is ₹7,290\displaystyle ₹ 7,290 if its value decrease every year by 10%\displaystyle 10\% then its value before 3\displaystyle 3 years is equal to:

Options

A10,000\displaystyle 10,000
B10,500\displaystyle 10,500
C20,000\displaystyle 20,000
D20,500\displaystyle 20,500
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Correct Answer

✅ Option a — 10,000\displaystyle 10,000

All Options:

  • A10,000\displaystyle 10,000
  • B10,500\displaystyle 10,500
  • C20,000\displaystyle 20,000
  • D20,500\displaystyle 20,500

Detailed Solution & Explanation

Let the value of the scooter 3\displaystyle 3 years ago be P0\displaystyle P_0. Given parameters: * Present Value (PV\displaystyle PV) = Rs. 7,290\displaystyle \text{Rs. }7,290 * Rate of depreciation (d\displaystyle d) = 10%\displaystyle 10\% p.a. =0.10\displaystyle = 0.10 * Time (n\displaystyle n) = 3\displaystyle 3 years The formula for depreciated value is: PV=P0(1−d)nPV = P_0 (1 - d)^n Substituting the values: 7,290=P0(1−0.10)37,290 = P_0 (1 - 0.10)^3 7,290=P0(0.9)37,290 = P_0 (0.9)^3 7,290=P0×0.7297,290 = P_0 \times 0.729 Solving for P0\displaystyle P_0: P0=7,2900.729=10,000P_0 = \frac{7,290}{0.729} = 10,000 Thus, the value of the scooter 3\displaystyle 3 years ago was Rs. 10,000\displaystyle \text{Rs. }10,000. Hence, **Option A** is the correct answer.

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