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A piece of equipment costs Rs. 600000 in a certain factory. If it depreciates in value 1% the first year,13.5% the next year,12% the third year and so on. What will be its value at the end of 10 years, all percentages applying to the original costs?

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Rs 125000

Rs 115000

Rs 100000

Rs 105000

answer is D.

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Detailed Solution

Given, A piece of equipment costs Rs. 600000
To find Value of the equipment of the end of 10 years
A.P. will be 15, 13.5, 12,……………………………..up to 10 terms
Hence,
First term, a = 15,
Common difference, d= 13.5-15 = -1.5
By Formula

S_{n} = \frac{n}{2} {2 a + (n - 1) d}

Where a is first term, d is common difference and n is number of term in an A.P.
Therefore,
Total percentage of depreciation in 10 years,

S_{10} = \frac{10}{2} {2 \times 15 + (10 - 1) \times - 1.5}

\Rightarrow S_{10} = 5 (30 + 9 \times - 1.5)

\Rightarrow S_{10} = 5 (30 - 13.5)

\Rightarrow S_{10} = 5 (16.5)

\Rightarrow S_{10} = 82.5

Value of the equipment at the end of 10 years,

= \frac{100 - Depreciation %}{100} \times cost of equipment

= \frac{100 - 82.5}{100} \times 600000

= \frac{175}{10} \times 6000

= 175 \times 600

= Rs 105000

Correct option is 4.

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