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# Question 68. A piece of equipment cost a certain factory Rs 600,000. If it depreciates in value, 15% the first, 13.5% the second 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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This is an arithmetic progression based question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise – 9.6
In this question we have been given that a piece of equipment cost a certain factory Rs 600,000

If it depreciates in value, 15% the first, 13.5% the second year, 12% the third year and so on.

Niw we have to find what its value will be at the end of 10 years, all percentages applying to the original cost.

This is very conceptualÂ  and important question.

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 68

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1. Cost of equipment = Rs 600,000

Depreciation value in first year = 15% of 600,000 = 90,000

Depreciation value in second year = 13.5% of 600000 = 81,000

Depreciation value in third year = 12% of 600000 = 72,000

So, first term(a) = 90000 and common difference(d) = 81000 â€“ 90000 = â€“9000.

By using the formula of the sum of n terms of an A.P.

SnÂ = n[2a +(n â€“ 1)d] / 2

Total Depreciation amount in 10 years = S10

= 10[2(90000) + (10 â€“ 1)(â€“9000)] / 2

= 5[180000 â€“ 81000]

= 5[99000]

= Rs 495,000

Value of equipment = Cost â€“ Depreciation at end of 10 years

= 600000 â€“ 495000

= Rs 105000

Hence, value at the end of 10 years is Rs 105000.

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