Question

# A piece of equipment costs a certain factory $$Rs. 600,000.$$ If it in value, $$15\%$$ the first, $$13.5\%$$ the next year, $$12\%$$ the third year and so on. What will be it's a value at the end of $$10$$ years, all percentages applying to the original cost

A
125000
B
115000
C
100000
D
105000

Solution

## The correct option is C $$105000$$The percentage of depreciation at the end of 1st, 2nd  and 3rd year are $$15 \%, 13.5 \%,12\%$$ which are in A.P with $$a= 15\%$$ and $$d= -1.5\%$$.Hence, percentage of depreciation in the 10th year $$= a+\left(10-1\right) d = 15+\left(10-1 \right) \times (-1.5) = 1.5$$Also total value depreciation in 10 year $$= 15+13.5+12+...+1.5 = 82.5$$Hence, the value of equipment at the end of 10 years $$= 100-82.5 = 17.5$$$$\%.$$The total cost at the end of 10 years$$= Rs. \dfrac{17.5}{100}\times 600000 = Rs. 105000$$.Mathematics

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