Arithmetic Progression  CAT 2016 Quant / Math Preparation
Question 4 the day : March 25, 2003
The question for the day is from the topic Progressions. It is an Arithmetic Progression question where the common difference is negative.
Question 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?
(1) 2,00,000
(2) 1,05,000
(3) 4,05,000
(4) 6,50,000
Explanatory Answer
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 = 15 and d =  1.5.
Hence, percentage of depreciation in the tenth year = a + (101) 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. 6,00,000/100 * 17.5 = Rs. 1,05,000.
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