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Misc 31 - A manufacturer reckons that value of a machine - Geometric Progression(GP): Statement

Misc 31 - Chapter 9 Class 11 Sequences and Series - Part 2
Misc 31 - Chapter 9 Class 11 Sequences and Series - Part 3 Misc 31 - Chapter 9 Class 11 Sequences and Series - Part 4


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Misc 31 (Method 1) 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. We use the formula A = P ("1 –" 𝑟/100)^𝑛 Here, P = principal r = rate of depreciation n = number of years A be the depreciated value Putting values Depreciated value = 15625("1 " −20/100)^5 = 15625("1 " −1/5)^5 = 15625("1 " −1/5)^5 = 15625 (4/5)^5 = (15625 × 1024)/3125 = 5 × 1025 = 5125 Thus, the depreciated value of the machine after 5 years is Rs. 5125 Misc 31 (Method 2) 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. The series is 12500 , 10000, 8000,….. This is a G.P. as 10000/12500 = 0.8 & 8000/10000 = 0.8 So, common ratio = 0.8 & first term = a = 12500 We need to calculate amount at the end of 5th year i.e. a5 We know that nth term of GP is an = arn – 1 Putting a = 12500, r = 0.8, n = 5 a5 = 12500(0.8)5 – 1 = 12500(0.8)4 = Rs. 5120 Hence value of machine after 5 years is Rs. 5120

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.