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Question

Shamshad Ali buys a scooter for Rs 22000. He pays 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?

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Solution

Given Shamshad Ali buys a scooter for Rs. 22000 and pay Rs4000 in cash Unpaid amount =220004000=Rs18000.
At the end of first year , interest paid =10% of 18000
Amount paid as instalment at the end of 1 year =Rs1000.
So, loan amount left =Rs180001000=Rs17000

Now, at the end of second year , interest paid 10% of 17000
Amount paid as instalment at the end of second year = Rs1000
So, loan amount left =Rs170001000=Rs16000

So, total interest to be paid =10% of 18000+10% of 17000+10% of 16000+...+10% of 1000.
=10% of (18000+17000+16000+...1000)
=10% of (1000+2000+3000+...+18000) ....(1)
Here, 1000, 2000, 3000, ...18000 forms an A.P. with both the first term and common difference equals to 1000.
Let the number of terms of A.P.be n.
18000=1000+(n1)(1000)
n=18
S18=1000+2000+...+18000
=182[2(1000)+(181)(1000)]

=9[2000+17000]=171000
So, by eqn(1),
Total interest paid =10% of (18000+17000+16000+...+1000)$
=10% of Rs.1,71,000
=Rs.17,100
So, the cost of scooter to him is Rs.22000+17100=39100

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