Miscellaneous

Chapter 8 Class 11 Sequences and Series
Serial order wise

### Transcript

Misc 14 Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual installment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him? Amount paid to buy scooter = Rs 22000 He pay cash = Rs 4000 Remaining balance = Rs 22000 – Rs 4000 = Rs 18000 Annual instalment = 1000 + "Interest on unpaid amount @10%" Thus , our instalments are 2800 , 2700 , 2600,… Total number of instalments = (𝑅𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑏𝑎𝑙𝑎𝑛𝑐𝑒 𝑙𝑒𝑓𝑡)/(𝐵𝑎𝑙𝑎𝑛𝑐𝑒 𝑐𝑙𝑒𝑎𝑟𝑒𝑑 𝑝𝑒𝑟 𝑖𝑛𝑠𝑡𝑎𝑙𝑚𝑒𝑛𝑡) = 18000/1000 = 18 So, our instalments are 2800 , 2700 , 2600 , … to 18 terms We can observe that this is an AP as difference between consecutive terms is an AP Here first term (a) = 2800 common difference = d = 2700 – 2800 = – 100 number of terms = n = 18 We need to calculate total amount paid in 18 instalments i.e. (2800 + 2700 +2600 + … to 18 terms) We use the formula, Sn = 𝑛/2 (2a + (n – 1)d) Where, Sn = sum of n terms of A.P. n = number of terms a = first term and d = common difference Putting value of n = 18 , a = 2800 & d = –100 S18 = 18/2 [ 2(2800)+(18 – 1) (-100) ] = 9[ 5600 + 17(-100)] = 9[ 5600 – 1700] = 9(3900) = 35100 Hence, amount paid in 18 instalments = Rs 35100 Total amount paid by him = Amount paid earlier + Amount paid in 18 instalments = 4000 + 35100 = Rs 39100

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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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.