A piece of equipment cost a certain factory Rs $600, 000$ . If it depreciates in value, $15$ % 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 cost?

Rs 2,00,000

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Rs 1,05,000

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Rs 4,05,000

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Rs 6,50,000

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Solution

The correct option is B Rs 1,05,000
Let the cost of an equipment is Rs. $100$ .
Now the percentages of depreciation at the end of $1 s t, 2 n d, 3 r d$ years are $15, 13.5, 12$ , which are in A.P., with $a = 15$ and $d = - 1.5$ .
Hence, percentage of depreciation in the tenth year $= a + (10 - 1) d = 15 + 9 (- 1.5) = 1.5$
Also total value depreciated in $10 y e a r s = 15 + 13.5 + 12 + . . . + 1.5 = 82.5$
Hence, the value of equipment at the end of $10 y e a r s = 100 - 82.5 = 17.5$ .
The total cost being Rs. $6, 00, 000 / 100 \times 17.5 = R s . 1, 05, 000.$

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A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% 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 cost?

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