NCERT Solutions
Class 11 Maths
Sequences and Series

Ex.Misc.Q.28
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?
It is given that Shamshad Ali buys a scooter for Rs 22000 and pays Rs 4000 in cash.
So, Unpaid amount = Rs 22000 – Rs 4000 = Rs 18000
According to the given condition, the interest paid annually is
10% of 18000, 10% of 17000, 10% of 16000 … 10% of 1000
Thus, 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)
Here, 1000, 2000, 3000 … 18000 forms an A.P. with first term and common difference both equal to 1000.
Let the number of terms be n.
So, 18000 = 1000 + (n – 1) (1000)
n = 18
Now, 1000 + 2000 + 3000 + ………. + 18000
= (18 ÷ 2) [2 × 1000 + (18 - 1)1000]
= 9[2000 + 17 × 1000]
= 9[2000 + 17000]
= 9 × 19000
= 171000
Total interest paid = 10% of (18000 + 17000 + 16000 + … + 1000)
= 10% of Rs 171000
= (10 ÷ 100) × Rs 171000
= Rs 17100
Thus, the cost of scooter = Rs 22000 + Rs 17100 = Rs 39100