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?

2, 00, 000

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1, 05, 000

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4, 05, 000

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6, 50, 000

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Solution

The correct option is D $1, 05, 000$
Let the cost of an equipment is Rs. 100.
Now the percentages of depreciation at the end of 1st, 2nd, 3rd years are 15, 13.5, 12, which are in A.P., with a = 1.5 and d = - 1.
Hence, percentage of depreciation in the tenth year = a + (10-1) d = 15 + 9 (-1.5) = 1.5
Also total value depreciated in 10 years = 15 + 13.5 + 12 + ... + 1.5 = 82.5
Hence, the value of equipment at the end of 10 years=100 - 82.5 = 17.5.
The total cost being Rs. $\frac{600000}{100} \times 17.5 = 105000$ Rs

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