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NCERT Class XI Mathematics - Sequences and Series - Solutions

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Question : 109 of 106
Marks: +1, -0
A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.
Solution:  
Cost of machine = Rs. 15625
It will depreciate each year by 20%
∴ Cost of machine at the end of first year = Rs. (15625−15625×20100)\left(15625-\frac{15625\times 20}{100}\right)
= Rs. (15625 – 3125) = Rs. 12500.
Cost of machine at the end of second year = Rs. (12500−12500×20100)\left(12500-\frac{12500\times 20}{100}\right)
= Rs. [12500 – 2500] = Rs. 10000
Cost of machine at the end of third year = Rs. (10000−10000×20100)\left(10000-\frac{10000\times 20}{100}\right)
= Rs. [10000 – 2000] = Rs. 8000
Cost of machine at the end of fourth year = Rs. (8000−8000×20100)\left(8000-\frac{8000\times 20}{100}\right)
= Rs. [8000 – 1600] = Rs. 6400
Cost of machine at the end of fifth year = Rs. (6400−6400×20100)\left(6400-\frac{6400\times 20}{100}\right)
= Rs. [6400 – 1280] = Rs. 5120.
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