NCERT Solutions
Class 11 Maths
Sequences and Series

Ex.Misc.Q.27
A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in
annual installments of Rs 500 plus 12% interest on the unpaid amount.
How much will be the tractor cost him?
It is given that the farmer pays Rs 6000 in cash.
Therefore, unpaid amount = Rs 12000 – Rs 6000 = Rs 6000
According to the given condition, the interest paid annually is 12% of 6000, 12% of 5500, 12% of 5000, ……..., 12% of 500
Thus, total interest to be paid
= 12% of 6000 + 12% of 5500 + 12% of 5000 + … + 12% of 500
= 12% of (6000 + 5500 + 5000 + … + 500)
= 12% of (500 + 1000 + 1500 + … + 6000)
Now, the series 500, 1000, 1500 … 6000 is an A.P. with both the first term and common difference equal to 500.
Let the number of terms of the A.P. be n.
So, 6000 = 500 + (n – 1) 500
1 + (n – 1) = 12
n = 12
Sum of the A.P = (12 ÷ 2) [2 × 500 + (12 - 1)500]
= 6[1000 + 5500]
= 6 × 6500
= 39000
Thus, total interest to be paid = 12% of (500 + 1000 + 1500 + … + 6000)
= 12% of 39000
= (12 ÷ 100) × 39000
= Rs 4680
Thus, the cost of tractor = (Rs 12000 + Rs 4680) = Rs 16680