Mathematics for FinancePYQ Dec 23Question 1254 of 512
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A machine costing 1,00,000\displaystyle 1,00,000 has useful life of 10\displaystyle 10 years. If the rate of depreciation is 12%\displaystyle 12\% what is scrap value of the machine at the end of life? Given (0.88)10=0.27850\displaystyle (0.88)^{10} = 0.27850

Options

A25,850\displaystyle 25,850
B26,850\displaystyle 26,850
C27,850\displaystyle 27,850
D28,850\displaystyle 28,850
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Correct Answer

✅ Option c — 27,850\displaystyle 27,850

All Options:

  • A25,850\displaystyle 25,850
  • B26,850\displaystyle 26,850
  • C27,850\displaystyle 27,850
  • D28,850\displaystyle 28,850

Detailed Solution & Explanation

**Derivation of Scrap Value** Given: - Initial Cost of Machine (V0\displaystyle V_0) = Rs. 1,00,000\displaystyle \text{Rs. }1,00,000 - Useful Life (t\displaystyle t) = 10\displaystyle 10 years - Rate of Depreciation (d\displaystyle d) = 12%\displaystyle 12\% per annum - Given: (0.88)10=0.27850\displaystyle (0.88)^{10} = 0.27850 **Step 1: Calculate Scrap Value (Vt\displaystyle V_t)** Vt=V0(1−d)tV_t = V_0(1 - d)^t V10=100000(1−0.12)10V_{10} = 100000(1 - 0.12)^{10} V10=100000(0.88)10V_{10} = 100000(0.88)^{10} Using the given value: V10=100000×0.27850=Rs. 27,850V_{10} = 100000 \times 0.27850 = \text{Rs. }27,850 Hence, **Option C** is the correct answer.

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