Given Shamshad Ali buys a scooter for Rs. 22000 and pay Rs4000 in cash ⇒ Unpaid amount =22000−4000=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 =Rs18000−1000=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 =Rs17000−1000=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+(n−1)(1000)
⇒n=18
∴S18=1000+2000+...+18000
=182[2(1000)+(18−1)(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