Mathematics for FinancePYQ Nov 18Question 1278 of 512
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The value of a machine depreciates 12%\displaystyle 12\% annually. If the present value of 68,150\displaystyle 68,150 then its value in 3\displaystyle 3 years ago was.

Options

A1,10,000\displaystyle 1,10,000
B1,00,004\displaystyle 1,00,004
C92,000\displaystyle 92,000
D97,900\displaystyle 97,900
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Correct Answer

✅ Option b — 1,00,004\displaystyle 1,00,004

All Options:

  • A1,10,000\displaystyle 1,10,000
  • B1,00,004\displaystyle 1,00,004
  • C92,000\displaystyle 92,000
  • D97,900\displaystyle 97,900

Detailed Solution & Explanation

**Derivation of Original Value (3 Years Ago)** Given: - Present Value (Vt\displaystyle V_t) = Rs. 68,150\displaystyle \text{Rs. }68,150 - Rate of Depreciation (d\displaystyle d) = 12%\displaystyle 12\% annually - Time (t\displaystyle t) = 3\displaystyle 3 years **Step 1: Set up the depreciation formula** Vt=V0(1−d)tV_t = V_0(1 - d)^t 68150=V0(1−0.12)368150 = V_0(1 - 0.12)^3 68150=V0(0.88)368150 = V_0(0.88)^3 68150=0.681472V068150 = 0.681472 V_0 **Step 2: Solve for V0\displaystyle V_0** V0=681500.681472≈Rs. 1,00,004V_0 = \frac{68150}{0.681472} \approx \text{Rs. }1,00,004 Hence, **Option B** is the correct answer.

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