Mathematics for FinancePYQ Jun 23Question 1246 of 512
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A machine depreciates 10%\displaystyle 10\% of its value at the beginning of the year. The cost and scrap value realized at the time of sale being 23,240\displaystyle 23,240 and 9,000\displaystyle 9,000 respectively. Approximately, for how many years the machine is put to use?

Options

A7
B8
C9
D10
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Correct Answer

✅ Option c — 9

All Options:

  • A7
  • B8
  • C9
  • D10

Detailed Solution & Explanation

**Derivation of Machine Use Period** Given: - Cost of Machine (V0\displaystyle V_0) = Rs. 23,240\displaystyle \text{Rs. }23,240 - Scrap Value (Vt\displaystyle V_t) = Rs. 9,000\displaystyle \text{Rs. }9,000 - Rate of Depreciation (d\displaystyle d) = 10%\displaystyle 10\% per annum **Step 1: Set up the depreciation equation** Vt=V0(1−d)tV_t = V_0(1 - d)^t 9000=23240(1−0.10)t9000 = 23240(1 - 0.10)^t 900023240=(0.9)t\frac{9000}{23240} = (0.9)^t 0.387263=(0.9)t0.387263 = (0.9)^t **Step 2: Solve for t\displaystyle t by evaluating powers of 0.9\displaystyle 0.9** - (0.9)8≈0.430467\displaystyle (0.9)^8 \approx 0.430467 - (0.9)9≈0.387420\displaystyle (0.9)^9 \approx 0.387420 Since (0.9)9=0.387420≈0.387263\displaystyle (0.9)^9 = 0.387420 \approx 0.387263, the period is approximately 9\displaystyle 9 years. Hence, **Option C** is the correct answer.

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