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A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?

  • A.Rs.25600.24
  • B.Rs.32000.50
  • C.Rs.18060.36
  • D.Rs.18600

Answer: A

A yearly fall of \( 6\tfrac{1}{4}\% = \tfrac{1}{16} \) leaves \( \tfrac{15}{16} \) of the value each year.

\[ P \times \left(\frac{15}{16}\right)^{3} = 21093 \]

\[ P = 21093 \times \frac{16^{3}}{15^{3}} = 21093 \times \frac{4096}{3375} \]

\[ = \text{Rs. } 25{,}600.24 \]

Depreciation is compound too, so the value must be divided by the yearly factor - adding back three lots of 6.25% would give a different and smaller figure.

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